{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/pinecone-io/examples/blob/master/learn/search/faiss-ebook/locality-sensitive-hashing-random-projection/hyperplanes.ipynb) [![Open nbviewer](https://raw.githubusercontent.com/pinecone-io/examples/master/assets/nbviewer-shield.svg)](https://nbviewer.org/github/pinecone-io/examples/blob/master/learn/search/faiss-ebook/locality-sensitive-hashing-random-projection/hyperplanes.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import spatial\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will start with a few simple 2D vectors that we can visualize easily."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, 20],\n",
       "       [13, 10],\n",
       "       [12, 11]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points = np.asarray([[1, 20], [13, 10], [12, 11]])\n",
    "points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.0, 20.5)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(points[:,0], points[:,1])\n",
    "plt.xlim(0)\n",
    "plt.ylim(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will perform the splitting of our vectors by randomly creating new vectors which will act as the normal of a hyperplane centred at the origin *(0, 0)*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def hash_vec(dim):\n",
    "    return np.random.rand((dim)) - .5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.30298326, -0.36059008])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h_vec = hash_vec(2)\n",
    "h_vec"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's first see if we can use this normal vector alongside the dot product to seperate our three vectors. The dot product will return a positive value if two vectors share the same direction, and a negative value if not (in the unlikely case of them being perfectly perpendicular the dot product value would be *0*)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def direction(vec, hash_vec):\n",
    "    if np.dot(vec, hash_vec) > 0:\n",
    "        return 1\n",
    "    else:\n",
    "        return 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "for xy in points:\n",
    "    print(direction(xy, h_vec))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have a functioning way of splitting our vectors now, but using a single split gives us very little indication about which vectors are similar or not - indeed, we would return only two buckets, *0* and *1* grouped vectors.\n",
    "\n",
    "So, we need more hash functions - and the more we use, the better our LSH performance. Although we also want to balance this against search speed as the more buckets we use, the greater our search times. We will define the number of hyperplane splits using the variable `nbits`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.17632542, -0.28834479],\n",
       "       [ 0.43623557,  0.23499209],\n",
       "       [-0.37562719, -0.01141066],\n",
       "       [-0.35437951, -0.12003665],\n",
       "       [ 0.03774678, -0.09317542],\n",
       "       [ 0.08486487,  0.08708127],\n",
       "       [-0.22617495,  0.36291174],\n",
       "       [-0.37251004, -0.47769561]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nbits = 8\n",
    "hash_vecs = []\n",
    "\n",
    "for n in range(nbits):\n",
    "    hash_vecs.append(hash_vec(2))\n",
    "\n",
    "hash_vecs = np.stack(hash_vecs)\n",
    "hash_vecs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's visualize these hyperplanes alongside our original three points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-5.0, 22.0)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GYSw3TXNKZ54TEy0WhsNB1g03ENi1i7r7H7A6jhymhrYGtjVsszqGiIiISKfERIEMkDh7Fp5jjqbm3/8muGeP1XHkMNy57k4WPq2TEEVERCS2xEQP8j7Z3/8+zW+/gy0x0eoochg8Tg/BcJBAKIDT7rQ6joiIiMhhiakCOW7oUOKGDrU6hhwmj9MDgC/gw2v3WhtGRERE5DDFTIvF/hpfeIHym35qdQw5BLfDDYAvqFFvIiIiEjtiskAOlJZS/+ij+N591+oo8gX230EWERERiRUxWSCnXnopzoICKn/3e8xQyOo48jlGZ4zmphk3kZmQaXUUERERkcMWkwWyLS6OrO/9H20bN1K/aJHVceRz5Cfmc+6wc0mNT7U6ioiIiMhhi8kCGSBp/nwSJk2i+m9/J+zTW/i9UXuonfU169nTqrF8IiIiEjtitkA2DIPsH/2QnJt+guF2Wx1HDqK6pZoLnruAt3a9ZXUUERERkcMWU2PePi1h9GgSRo+2OoZ8jn1TLPxBv8VJREREpL8xTRPDMI7ouTG7g7y/2ttvp/wnN1kdQz5FUyxERESkpwWq/DS8sI2KPywj5Asc0RoxvYO8T6i5mfrHHsN7ztkkjB9vdRzZy2V34bA5VCCLiIhItwq3BvGvqsa/vJL2XU1gg/jhaZgtwSNar0/sIKd/6RrsmRlU3vw7TNO0Oo7sx+P0qEAWERGRqDPDJqHmdgDCvgD1T20m3B4i5dRB5P5gGhmXj8aRkXBEa/eJHWR7ooesb32L8h//hKaXXiL5pJOsjiR7/XzGz8lNzLU6hoiIiPQRgSo//uWV+FZW4SpMIuPSUTjSE8j+7mQcmQlH3He8P8OKHdcpU6aYy5Yti+qaZijEtoVnE/b7GfLiCxh2e1TXFxERERHr+NdU0/xO6SctFMPS8ByVTcLojC98nmEYy03TnNKZa/WJHWQAw24n95e/AJtdxXEv8vGej2kPtTMuc5zVUURERCSGmGGTtpI64oZ4MRw2glX+jhYK94Qs7Emubrt2nymQARLGfVKEdWW0h0TPn5f9GV/AxwOnPmB1FBEREYkBgSo/vuWV+FdUEW5qJ/3SkSSMziBpbiFJxw/okfquTxXIECmMK276KYbTQc5NGv1mNY/TQ5W/yuoYIiIi0suFmtupuecjAvtNofBMziZ+eBoAhr3nZkv0uQLZMAwMl4u6hx4i9cILiSsutjpSv+Z2uvEFNcVCREREDmSGTFo31xFuCuCZko3N48Se6MR96mDcEzK7tYXiUPpcgQyQcd3XaXj6aSp//wcG/Pc2q+P0axrzJiIiIvsLVPrwrajqaKFwZCTgnpyFYRhkXN47TkjukwWyIzWVjK9+larf/57md94h8eijrY7Ub3mcHvwBv3rCRUREhMbXdtL4yo4DWyhGpPW6GqFPFsgAqZdcTN3DD1P9j1tUIFvozCFnMjVnqtUxREREpIfta6HwL68k6ZgCXAVJkWLYZev2KRRd1WcLZJvLRf4f/4AjO9vqKP1aUUoRRSlFVscQERGRHhKo9OFbXoV/ZaSFwuZ2kDAmA1dBEq78RFz5iVZHPKQ+WyDDJ2PfTNOEYBDD6bQ4Uf9T6atkVfUqZuXNItHV+/9AiIiISOeZYRPDZmAGw1T9ezVme+jAFgpHz02giIY+XSADmIEAO790DQnjxpH1f9+1Ok6/s7ZmLd9763s8dvpjjEgbYXUcERERiRIzZNJaEmmhCNa0kPXNiRgOG+kXj8SZ4+nVLRSH0ucLZMPpxJmTw5577sF7/vm4CvKtjtSvuJ1uAE2yEBER6SOCtS00v1+Bf2Ul4aYANrcD94QsCIbBaSe+ONXqiF0WW/vdRyjzO98Gm43qP//J6ij9jsfpAVQgi4iIxLKwP0DYHwCgvbSZ5sWluAqTSb90JLk/nIb3jCEYTrvFKaOnz+8gAzhzcki/6ipq/vUvUi+9FPfEiVZH6jc8jkiB7A/6LU4iIiIinbF/C0XLR7UknzCA5LkDSBiVTu4Pp2JPjN0WikPpFzvIAOlXX4UjM5Pa2++wOkq/sm8H2R9QgSwiIhILTNOk4cXtlN/8PrV3r6dtaz2J03NJGJkOgOGw9eniGPrJDjKAzeOh8Nb/4CoqsjpKv5KRkMG9J9/LwOSBVkcRERGRzxH2B2jb2kDCmAwMwyBQ7cdVmIxnchbxw2NvCkVX9ZsCGSB+1CgAzPZ2TCKzkqV7Oe1OJmappUVERKS3+XQLBSGTnB9MxZESR/rFIzFsvet0u57UrwpkgFBjI9vOPRfvwrPJ+PK1VsfpF57b+hz5iflMyJpgdRQRkV7nqZWl/OGljZTVt5DnTeD6+cNZMFETl6R7tW1toPahDZEpFB4HidNzcU/OxpESB9Cvi2PohwWyPTmZuKHF1N56K96zF+LIyLA6Up/3+w9/zwkDTlCBLCLyKU+tLOUHi9bSEggBUFrfwg8WrQVQkSxRFfYH8K+uxp4aT8KINBxZCf26heJQ+uV3I/v67xFub6f67/+wOkq/4Ha48QU15k1E5NP+8NLGjuJ4n5ZAiD+8tNGiRNKXmCGTlo/3UPvABsp+/T71/9tC6/paAOyJLjIuG0XC6AwVxwfR73aQAVxFRaRdfBF77ruf1IsvJn74MKsj9Wkep0dzkEVEDqKsvqVTHxfpjJq719FWUn9AC4UrL9HqWDGh375kyPjqV7ElJVH/6KNWR+nz3E63xryJiBxEnjehUx8X+TwhX4DmpWVU/Wc14bYgAImz8km/dBS5P5iG9/QhKo47oV/uIAPYvV6KHnpQY996gNvppr613uoYIiK9zvXzhx/QgwyQ4LRz/fzhFqaSWHGwKRTOPA+h+jZs2Q4SRqRZHTFm9dsCGSBu8GAAgnV12BMTMZxOixP1TT+Z/hNs/ffNChGRz7XvRjxNsZDOMINhDIeNYLWf2rvXq4WiGximafb4RadMmWIuW7asx697MO27S9m2cCGZ3/4WaRddZHUcERERkc8I+QK0rK7Gt7wSZ2YCaReMAKB1cx1xRSm60e4LGIax3DTNKZ15Tr/eQQZw5ucRP3IkNf+4hZTTTsOenGx1pD5nZdVK1lav5bLRl1kdRUREJKa0bq7D9145LRv2RFoocj24BqV0fD5+aKqF6fqufv9ywzAMsm/4PqH6empuvdXqOH3S4tLF/HHZH7Hi3QoREZFYE6jwYYYjPzNbN9XTtq2RxBl5ZH1zItnfmkTitFyLE/Z9/X4HGSJHUKecdRZ1995H6gUX4CostDpSn+JxejAxaQm24Ha6rY4jIiLS6+zfQhEobSbjqjHED0sl+bhCUuYPxLD3+z3NHqXv9l6Z3/oWOJ00vfqa1VH6HI/DA6BZyCIiIp8S8gWovf8jyn/zPvVPbwHTJOX0wTjzIzfb2eIdKo4toB3kvZzZWQx54Xmc2dlWR+lz9u0a+wI+Msm0OI2IiIi1AhU+gvVtJIxIw5bgIFjbSuKMPNyTsjSFopdQgbyffcVx+86dOAsKMGx6xRYNHufeHWQdNy0iIv1UyBegZVUVvhVVBEqbsXvjiL/hKAybQdY3J2IYhtURZT8qkD+lZc0atl90MXm/+TUpZ5xhdZw+YUbeDF4/93VS43WnrYiI9D9Ni0tpeGFbZApFfiLe0weTMCGroyhWcdz7HHaBbBjGncBpQJVpmmP2fiwNeAQoArYD55mmWRf9mD0nfswY4ocPp+rPfyFp3jxsCTrus6sSHAkkOPR9FBGR/iFQ4cO3rBLPUdk4sz248hIjLRSTs3HleqyOJ4ehMz0EdwMnfepjNwKvmaZZDLy29/cxzbDZyL7xBoIVFey5+26r4/QJDW0N/GvVv9hQu8HqKCIi/dpTK0uZdfPrDLrxOWbd/DpPrSy1OlKfEfIFaFpSSuU/VlL51xU0Ly2jfVczAHGDU/CeNljFcQw57ALZNM23gT2f+vCZwD17f30PsCA6sazlPuookubNo+a/txOoqrI6TsxrDbby79X/Zl3tOqujiIj0W0+tLOUHi9ZSWt+CCZTWt/CDRWtVJEeBGQxT8YdlNDyzFQDv6YPJ/eE0PFN043+s6updaNmmaZYD7P13Vtcj9Q5Z3/s/DKBlxQqro8S8fTfp+QN+i5OIiPRff3hpIy2B0AEfawmE+MNLGy1KFLvay33UP7uV6jsjGz+Gw0bqgiFkfWsS2d+YSOKsfOwep8UppSt67CY9wzCuBa4FGDBgQE9d9oi5Bg5k6Jtv6OjpKNh/zJuIiFijrL6lUx+XA316CgV2g4QRaZiBEIbTjntCn9kjFLq+g1xpGEYuwN5/f24/gmmat5mmOcU0zSmZmbExC3dfcdyyZo2OSe4Cm2EjwZGgAllExEJ53oPfLP15HxcwQ2HMvbvurRv2UP+pFor0S0dhOO1WRpRu0tUC+Wng8r2/vhz4XxfX63WaXn+d7eedT/Mbb1odJaa5HW78QbVYiIhY5fr5w0n4VDGX4LRz/fzhFiXqvfa1UJT/5gOa368AIGFsBtnfVgtFf2Ec7s6oYRgPAXOADKAS+CnwFPAoMADYCZxrmuanb+T7jClTppjLli07ssQ9zAwE2HrGmWCaDH76fxgul9WRYpIv4CPeHo/dplfaIiJWeWplKX94aSNl9S3keRO4fv5wFkzMtzpWr2CaJr53y/AtryRQ5utooUiclUfcYK/V8aQLDMNYbprmlE49x4rWgVgqkAGa3niD3V/9Gtk//CFpl11qdRwRERGJAjMUpr20mbgBkZbK6tvWEG4L4ZmcTcL4TO0S9xFHUiDrJL3DkDhnDu4Z06n+5z9JOeN07F6v1ZFizqMbH6Ul2MLloy8/9INFRES6UXu5D//ySvwrqwi3BMj9wTTsSS7SLx+NLU7vdErXe5D7BcMwyL7hBgyHg7YtW6yOE5Pe2v0Wz219zuoYIiLSj7XvaqLy7yuo+lvkII+4QcmkXzoKmzuyX6jiWPbRDvJhih8xgqFvvI5NPchHxOPwsCO4w+oYIiLSj5ihMK0f12HzOIgrSsGW5ASbgfeMIWqhkC+kArkTbC4XZiiE792lJB492+o4McXtdGvMm4iI9Ij2suZIC8WqasK+AAnjM4krSsHhjSf7uolWx5MYoAK5k+offZSKn/+CAffcg2faVKvjxAyP06MCWUREul3tAxtoWVsTmUIxKh335Gzii1OtjiUxxpoeZDNsyWWjIeWss3Dk5lL5u5sxw7H7dfQ0t9ONaZqEY/i/vYiI9C5mKEzL+lpqH/oYMxD5+RI/Mg3vmUMiB3lcPJKEEWkYdsPipBJrrBnzNjjNXLalFozY/B+24ZlnKbv+enJ/+1u8Zy2wOk5MME0TI0b/e4uISO/y6RYKW6KTjKvG4MpLtDqa9EKxM+Yt3huzxTFA8qmnsOe++6j+y19Inn8iNrfb6ki9nopjERHpin0bLe1lzVT9feVnWii0SyzRZE2LhTst8u/6XZZcvqsMm43sG2/AlpREoKLC6jgxYX3Nen74zg+p8On7JSIih8cMhmlZX0PNvR9R/7/ImFVnrofUc4ephUK6lXVzkEuXwz8mw4d3WBahK9yTJjH4maeJGzzY6igxobqlmme2PkNNS43VUUREpJdrL/dR/8wWyn/7PrX3baB9ZyP2xMhINsMw8EzO1og26VbWTbHIGQ9D5sLz34PEbBh5mmVRjpRhsxFq9uFbvJjkk+ZbHadX8zg9AJpkISIiBxVqbsfmcWIYBr4PyvF9UKEWCrGMdTvIdgeccyfkTYInroYdSy2L0hV77ryT0u98h5b1662O0qu5nZE+bRXIIiKyz/4tFOW/+YD2HY0AJM8dQN6P1EIh1rH2qGmXBy56FFIK4KHzoX6npXGORNqVV2BPTaXq5t9hxUSQWOFxaAdZREQiwi3BA1sodjWSODsfe3IcAPZkFza3WijEOtYfFOJJh0sWwaoHIbnA6jSdZk9KIvOb36DiZz+n+bXXSDrhBKsj9UqJrkSSXclWxxAREYuEmtsJ7mklbkAyhtOGf20NcYO9aqGQXsmaOchTppjLli07+Cfrd0FcEiR4ezRTV5jBIFsXLMAMBBjyzDMYLpfVkURERCxnBsO0frwH34oqWj/eg90bR871UzAMAzMYxnBY+0a29A+xMwf58wTb4O5TIGUAXPIEOOOtTnRYDIeD7BtuYM9ddxNqaMCRmWl1JBEREUv5Pqyg4YVthP1BbElOEmfn45mc1TEXX8Wx9Ga9q0B2xMHxP43ctPfktXDOXWCzW53qsCQefTSe2bN1IMYX+NHiHzE+czznDT/P6igiIhJloeZ2/CurSRidjiMtHluSi7ghaqGQ2NS7CmSAsedAUwW8/CN48UY4+fcxc+qeYRgESkvxL1tGyplnWh2n13mv7D3shl0FsohIH9HRQrG8ktaNdRA2MZwGidPzSBiRRsKINKsjihyR3lcgA8y8DprKYektkDMWJl1mdaLDVnvHHdQ9+hjxY8cRN3iQ1XF6FbfTjT/otzqGiIhEgRkMU/77Dwk3tkdaKI7OxzMpC2e2x+poIl3WOwtkgHm/hMQsGLXA6iSdkvH1r9Pwv6ep+uMfKfzXP62O06t4nB6NeRMRiVH7WigClT7SzhmG4bCRdHQ+jiw38UPVQiF9S+8tkG02mPWtyK/bfVC1AQo6dQOiJRzp6aR/5ctU/+nP+N57D8/06VZH6jU8Tg/+gHaQRURixcFaKJyFSYTbQ9hcdpKOjr3xrCKHIzZuIX3xRrjnDChdbnWSw5J22WU48/Ko/N3vMUMhq+P0GvmJ+aTGp1odQ0REvoBpmpjhyAhY37JKau/fQPvuZhKPzif7O5PI/voEbK7YuIFe5Ej1vjnIB9NUAXfMg3Y/XP0ypA/pvnBR0vjii/jeXUr2jTdgc7utjiMiIvKFQk3t+FdV4V9eiWdGHonTcgn7A7TvaiJOLRQSw45kDnJsFMgANZsjRXJ8SqRITszqnnAiIiL9hGmatK6v3dtCsQfC4CxMInlOAQmjM6yOJxIVR1Igx0aLBUDGULj4schu8lNfszrNYWtZtYr6J56wOkav8GTJk3zppS9ZHUNEpF8zTZPgnlYgMp606a3de1soCsj+7mSyvz5BxbH0GcHAkbW69t6b9A6mYApc+CB4B1qd5LDtufc+ml57Dc/MmThzc62OY6lKfyXvV7xPMBzEYYut//VERGLd/i0UgZoW8n44DZvbSdolI7EnutRCIX1CoC1ExdYGykrqKSupp3Jb4xGtEzs7yPsMOS7Sg2yasP7JyL97saz/+y6YJlV/+YvVUSzndkR6sTXqTUSk5wQqfNTcs57y375Pw3PbMJx2vKcNgb1HPTtS4lQcS8xqawlSs7sZiLw78sBP3+Ppv61i+QvbCbaHGDMn/4jWjd1tvI0vwGNXwKxvw7yfW53mcznz80m74gpqb7uNtEsvJWHsWKsjWcbjjAyP9wf8pMSlWJxGRKRvMk2TQJkPw27gzPGA3aC9tJmkowtwT87GmaUbxyV2tTS3d+wOl5XUU7O7meSMBC795QwMw2DGWUOIT3SSOzgFV8KRl7mxWyAPPxmmXAVL/grJeTDty1Yn+lzp115D/RNPUHnz7xh4/30YMXJ0drTtK5C1gywiEn0HtFBU+EkYl0H6RSNxZrrJvXEqhq1//uyR2Oarb6N8SwNDJmViGAZLF21hw7vl2J02cgYnc9Spg8gr9mKaJoZhMHxaTlSuG7sFsmHAKX+E5ip44YbIVIvRZ1md6qDsiYlkXf89glXVEAqBI3a/7V2RkZDBqPRR/fYFgohId6l7sgTfhxUQBteAJLxnDcU9LrPj8yqOJVb4G9vZ+VEtZZsiO8QN1S0AXHjTNNLyPIw/vpCRM3PJGpiM3dl9ncKxM+bt8wRa4N4FULkOvr0W3GnRWVdERKQXMk2TQGkz/jU1pMwfiGG30bS4lHBzO+5JaqGQ2GGaJg1VLZSV1JM7NIXUHA/bVlfz/L/XEud2kFfs7fgnoyARm/3ICuIjGfMW+1uZzgS48CGo+qjXF8emadL4/POYra14zz7b6jgiIhJDQk3t+FdW4VteSbDSDw4D97gMXAVJJM0+shuRRHpaoC3Ex0vLO3qI/Y3tAMw8eyipOR7yh6dywU+mkpbrsfSdj9gvkCFSGBfNjvx6wzOQOx68A6zNdBCGYdDw9NO0LF9B4ty5ONJ6d0EfbVX+Kq577Tq+PP7LHD/geKvjiIjEjPZyH1X/WHFgC8XYDGxup9XRRD5XOBSmZnczZSX1JCQ6GT49F8MGix8vwZ3komBkKnlDIzvE3uzIOx+ueAfp+YkWJ+8rBfI+LfXwv+sgMRuuerFX7ihnf//7bD3jTGpu+Sc5N/3E6jg9ymbY2LBnA1X+KqujiIj0WvtaKHzLK7G5naTMG4gz203yCQNJGJOhFgrp9da+uZvta2so39JAoDVyUMeQSVkMn56Lw2nnsl/PxJ3s6tX3JPWtAjnBCxc8APedBQ9dAJf9L9KC0YvEDRlC6vnnU/fII6RefBFxQ4ZYHanHaIqFiMjnO1gLheeoyB35hs0g+bje986o9G/B9hAV2xopK6mnqbaF4y8fBcDOj/bQtKeN4VNzOnqIPd64jud5UuI+b8leo28VyBBptVj438iM5Ce+BOfdCza71akOkHHd12l45hmqfv8HCm/9j9Vxeky8PR6bYcMf8FsdRUSkVzCDYbAbkRa8F7fjX155wBQKWxfmuIp0l83Lq1jz+i4qtzcSDplgQEZBIsFACIfTzklfHoP9CG+o6y365p+80Qug+Xfwwvfh4+dg1BlWJzqAIy2N7BtvxJYQ3zG3rz8wDAOPw6MdZBHp1/ZvoWhZXU3G1WNx5SeSNLeQpGML1EIhvUarL0D55k8O5Zh39Wi8WW6C7SHCYZPxxxeSV+wld0gKcfv1w8d6cQx9tUCGyMEhOeNg4AyrkxyU9+yFVkewxLTcaeQn6m5rEel/wm0hfO+X79dCYSNhdDqGI7JJ4szoXS2B0v/s27Sr3tXEa3dvoLasGUywO2xkD0qmvSUIwIgZuYyYkWtx2u7Vdwtk+KQ4Ll8DVRtg/PnW5vkUMxik9o47cWRn4V2wwOo4PeIvc/9idQQRkR5jBsME69sixa8Bja/txJntVguF9ApNe1oju8Ob6ynbVM/oo/OYcMIAPClxJCQ5mXZ65JS6rKJkHM7e1a7a3frHn8x3/hQZ/xafAsNPsjrNJ+x2mt9+m/bt20k6YR72RI/ViUREpItM0ySwO9JC4V9djT3ZRfa3J2Fz2cm5fgr2RJfVEaUfMk2TQGsIV4KDcCjMQ7/4gPrKyD1Brng7ucVektMj72K4k12c+e2JVsa1XP8okM/8J9TviNy4d/kzUHiU1YmASE9u9o03sP3c86i97TayvvsdqyN1u58s+QkNbQ38/bi/Wx1FRCTq/GtraHxlB8GqT1ooPJOzOz6v4lh6imma1JX79+4O11FWUk9Klpuz/m8SNruNQeMz8KTEkVfsJb0gEZuOIz9A/yiQ4xLhosfgjnnw4Hlw9cuQUWx1KgASxo4l+YzT2XP33aSefx7O/L7dn9vY1siupl1WxxARiQozGKZlQy1xRSnYk1wQCmOLt6uFQnpcOGxSX+knLTfybvRL/13HlhXVALhTXOQXeykY+cn5EDMXDrUkZ6zoP39yEzPh0kVw+zxY8jc48xarE3XI+s53aHrpZar+9Gfy//wnq+N0K4/TozFvIhLTPt1CYbYESTltMEmz80kYn4l7QpbVEaUfCIXCVO9soqyknvKSesq3NNDWEuTqPx5NvCdyat2A0enkFXtJyUzoNxOzoqX/FMgAaYMju8cphVYnOYAzN5ecm24ibmjfPzTE7XTjD6pAFpHYZAbDVN2ykkDF3haKMel4JmUTN9QLoCJEuk0oEKZyeyNpuR7iE5189E4Zbz+8CQBvtpshk7LIK/Zid0RGrA0al2Fl3JjXvwpkgPS9RWhzdeTmvXk/B4f1J7r0l7FvHqfmIItI7DADkRaKQIWPlBOLMBw24oal4ZmZF2mhiO9/P0alZ4QCYcq2RKZLlJXUU7mtkVAwzAlXjmL4tByKxmWQkOQir9iLO1m97dHWf/9k71gC7/8bfFWw8HawWT/UOuzzUXnz7/DMmknySb1o2kYUjUgbwZzCOYTCIey97IRDERE4eAuF3RtH0pxCbC473lMGWR1R+qC2liDlm+uJczvJHZKCv6mdp/+6CsOAzAFJjJmTT95QL/nDvAAkpcWTlBZvbeg+rP8WyKMXQN3P4NWfQVIuzP+1xYHAiI+nZe1afO++S+LcudjirN/ZjraTB53MyYNOtjqGiMjn8n1QQf2Tmz9poZicTdwQL4bu8pco27a6mtKNkTnENbuaME0YOjmL3CEpJKXFc8a3J5A9MBmXbvbscf37Oz7r29BYDktvgaQcmPkNS+MYdjvZN3yfnVdexZ577yXjmmsszSMi0tfta6HwL6/EPSkL9/gsEkalYxgGCeMy1EIhUeNraKOspB5/Yzvjj4vcC/XBs9uoq/CTMziZKacUkTcslexByR3PKRyR9nnLSTfr33/yDQNO+i00V8Dyu+GoL4HT2qM+PTNmkDh3LrX/uRXvwoU40tMtzRNtb+9+mxvfuZF7TrqH4tTeMWpPRPqXg7ZQpLgwAyYA9iQXnqk5FqeUvmDnR7VsXl5F2aZ6GqpbgMghHOPmFGDYDE7+8lg8KXHYnda3ecqB+neBDGCzw1m3QbvP8uJ4n6zrr2frGWdQ889/knPTTVbHiSq7YaepvUk36olIjwu3hbDFRe592PP4JoK1rbjHpONWC4V0kWmaNFS1RI5tLqnnmAuH4Yp3UL6lga0rq8kd6mXMsfnkFXvJKEjs+H8tOaN31B3yWSqQAZzxkX+C7fDC92HKlZA73rI4cYMHkffrX+E+qnec+BdNHmdkgLkKZBHpCfu3ULTtaCL3h1OxueykXzgCuzdOLRTSJTW7m1j+wo6O1gmAhCQnjTUtZBQkMWn+QKaeOkgvvmKQ/mbYX0sdlLwCHz8HX3oFUossi5Jy5plA5FVpX5qr6Xa6ARXIItK9grUtNL1Tin9VNWZrpIUicUYuBMPgsuPM8VgdUWJIOGxSs6upY4d41Kw8isZlYIahYmsDBSNSySv2klfsxZvt7vi57XRpWlOsUoG8v6TsyGl7d5wI9y2MHCrisW7QdrC6mrIbbiDtyitJPPpoy3JEk3aQRaS7hBrbMIMmjrR4wm0hfMsq1UIhXdLeGuSl/66nYks97a0hAJIzE2hrCQKQUZjIZb+Z2ac2siRCBfKnZQ6Hix6Be8+EB8+Dy58BlzU7DfaUFNpLS6n83e/wzJiB4Yj9/1wprhTOGHIGBUkFVkcRkT5g/xaK1k11uCdmkXbecFx5ieT9ZBq2uNj/e1O6X7A9ROW2Rso211O6qZ6UzATmXjICZ5ydUDBE8dQc8opTyBuaSmLqJyNYVRj3XYZpmj1+0SlTppjLli3r8et2yoZn4X9fg8v+B3kTLYvR+MorlH7jm+T89CZSL7zQshwiIr1Nw8vbaX63vKOFwj0pG/fkbJy68UkOIRQMdxzJ/NrdH7FpWSXhoAkGZBQkMmRiFlNOKbI2pESNYRjLTdOc0pnn6KX15xl5GhTNhgSvpTGSTjgB91FHUf33f5B82mnYk5IszRMtYTOMzdBYGxE5fKGGNvxra0icmRdplzAhYUSqWijkkFp9Acq3NFC2qY6yknoaa1u58vezsdkM0vISGT83cmRz7tAU4txOq+NKL6AC+YvsK47fvQXaGmHuD3s8gmEYZN14A9vPOZc9d91N5jetPcwkGo5/9HjmDpjLj6f/2OooItLLmYEwLR/V4lteSVtJHZgQNzAZV2ESKfOLrI4nvZS/sZ04twO7w8bq13ax+PESMMHmMMguSmbMMfmEAmFscXYmnjjA6rjSC6lAPhTThJqNsOJeSMyGo67u8QgJo0eT/5e/4Jk9u8ev3R2cdif+gN/qGCLSywUqfFT9Z83eFoo4kuYW4p6kFgr5rOa61o4JE2Ul9dRV+FnwnYnkD08lZ0gKU08bRP4wL1lFyTicmiwhh6YC+VAMA079CzRXwfPfixTJI0/r8RjJJ80HwAyHMWyx3ZqQ4EjQFAsR+YxQQxu+lVXY4uwkzsjDkenGPT6DhLEZxA1WC4VEmKZJY00Lhs0gOT2Byu2NPH5z5L4mV7yd3KFeRszIJSkjHoDsomSyi5K/aEmRz1CBfDjsDjjnTrjnDHjiarj0KRg4o8djtG3dyu5vfJPcX/4S9yTrbhzsKo/Tgy+oAllEwAyE9rZQVHW0UCSMyyBxRh6G3SD1LB1J39+Zpkldhf+AHWJffRvjTyhk9jnFZBQkMvvcYvKKvaQXJGLTCymJAhXIh8vlgYsehbtOguqPLSmQnTk5hJuaqLz5Zooefihmd5I9Tg9N7U1WxxARi+x/AFLdk5vxr6jqaKHwTMrGoRaKfi0cNqktbaa1OUDhyDQAnvzTClqbA7hTXOTvPZCjYO/n7A4b448vtDKy9EEqkDvDkw5ffidyLDVE+pN7cAaize0m8zvfofwHP6Dx+RdIOe3UHrt2NJ0w8AT1IIv0Q/taKPzLK0m/dBTOLDeJs/JxT8pSC0U/V7O7iZ0f7aG8pJ7yLQ20+YMkZyZw6S9nYBgGJ149mqT0eFIyEzR7WHqE5iAfqc2vwVu/i+wq9+AoODMcZvs55xKsr2PI889ji4/vsWuLiHSWGQzTsr7mgBYKV1Ey3lMH4yrsG2MrpXNCgTCVOxqp2NrAxHkDMAyD1+/bwIYl5Xiz3eQNTSFvWOTo5qQ0/YyTrtMc5J5k2KB0BTx8MVzyxCe7yt1+WRtZN97Azssup+Gpp0i94IIeuW40hcIh/EE/SS79cBTpi0zTJOwPYvc4MQNh9jxWgj3RqRaKfqyuwsemDyopK6mnclsjoWAYgMETMvFmuZlychHTzhiMJyXuECuJ9AztIHfF2scjN+2NWgDn3AU92BPcvHgJnhnTMeyxN67m7yv+zp3r7mTlpSv1VplIH7J/C4URZyf7usjNxIFKH45Mt1oo+on2lmDkUI6SOoqPyiGjIJGtq6p58da1ZBQmkTfMS97QyD/xiTqUQ7qfdpB72thzoKkcXv4xvJgNJ/+ux3qSE2fPAiDc3o7N5eqRa0aL2+kmZIZoC7UR79DbZyKxrnVzHU1vlx7QQuGZnN1xM54z22N1ROlmrb4Ay57fTllJPTW7mjBNsNkMUnM8ZBQkMmB0Gl/68zG4ElR2SGzQ/6ldNfMb0FQBrfVghsHouR1d/7Jl7P7mtxhw153EDx/eY9ftKo8z8sPSF/CpQBaJQaZp0r6zCWdmAja3k9CeNoJVfrVQ9BO+hraOcWupOW7GzS3E4bSx4d1yMgsTmXxKEfnFXrIHp+B0RX4mOpx20GaxxBAVyNEw75eRnWPDgFAwMje5B8QVF0MoROXNNzPgzjtjpl1hX4HsD/hJT0i3OI2IHK5gQxv+FZEWimBNC97TB0emUEzOwj0lWy0UfdySx0vYtqaGhqoWAJxxdkYdnQeAw2Xn6j/OxmaPzfGjIp+mAjka9vUe122H+8+Bk2+GoSd0+2XtKSlkfP3rVP7mNzS/9RZJc+Z0+zWjwePYu4Osw0JEYoIZDFNz70cHtFCkHltAwtgMAAwVRX2GaZo0VLV07BD7m9o545sTAPA3tZOa42H00fnkFXvJLEw8oCBWcSx9iQrkaEpIA0c8PHIZXPEs5E/q9kumXngBdQ8+SNXv/0DirFkYzt7/HtYQ7xC+Nv5rpMalWh1FRA5iXwtFoLyZxOl5GA4bdreDpOMG4JmUhSNdLRR9hRk2wQDDMFjzxm6Wv7Adf2M7AAlJTvKKvYRCYex2G/OuHG1xWpGeoykW0dZUAXfMg0ALXP0ypA3u/ku+/ga7v/Y1Cv71T5KOO67brycifdOnWyiMeAe5P5yKzRV703Lk4MJhk9rdzZRuqqOspJ7yzQ2cc+NkUjLdlCyrZPuaGvL2nlTnzXbHTOueyBc5kikWKpC7Q00J3HEixKfA1a9AYma3Xs40TVrXrSNh7NhuvU60hMIhaltr8Tg9Hf3IImIt3/JK6h7fFGmhGBSZQpEwNgNbnN5ojGWhYJhwyMQZZ6espI7n/rmG9tYQAMmZCeQVe5k8fyDebLfFSUW6j2Vj3gzD2A40ASEg2NkQfU5GceSEvdd/Cbbu33kxDKOjOA41NmJPTu72a3ZFlb+KE584kZ/P/DkLixdaHUek39nXQuFfXkn86HQShqcRNyhFLRR9QLA9ROW2Rso211O6qZ7KrQ1MO3MwE04YgDfbQ/FR2R1ziBNTNUVI5PNEc2tgrmmaNVFcL7YVHgWX/S8y2SLYHvm3vXv7gxtfeIHyH/2YQU89iWvAgG69Vle4nZGdCl9AN+mJ9KRgfRv+lZX4l1dFWiicNhzZbhgOjrR4UuYNtDqidFJ7a5CWpgApmQkEAyHuuH4xwbYQGJCen8io2XlkD0oBwJ3sYs7FIyxOLBIb9N5Zd9o39u2BcyA5Dxb8u1sPEkmYNBkTqPrjnyj4+9+67Tpdtf8cZBHpXmbYxLAZmKZJze1rCda04BqUTOqcArVQxKBWX2DvKXX1lG2qo3pXM3lDU1jw3Uk4nHamnzGYlMwEcoakEO/p/Tdti/RW0fqb0QReNgzDBG41TfO2KK0b++wOGDgL3vwNJOXCCT/ttks5s7NI/9LV1Pz9H/g//BD3UUd127W6wmFzEGePwx/wWx1FpE/av4WidXM9Od+djOGwkbpwKPaUOLVQxBB/Yzs1u5sYMCoyM/7lO9az66M92BwG2UXJTJo/gIIRaR2PH398oVVRRfqUaBXIs0zTLDMMIwt4xTCMj03TfHv/BxiGcS1wLcCAXvz2f7c49vuRI6kX/zlSJE+7ttsulX7lldQ/+hiVN/+OoscexbD1zrmUHqdHO8giURZqase3rOKAFoqEsRmEW4PYE13EDfZaHVEOwd/Yzu6P93TMIa6r8IMBX/rT0cS5nUw5uYjJJw0kuygZh6aLiHSbqBTIpmmW7f13lWEYTwJTgbc/9ZjbgNsgMsWivrICb3ZONC7f+xkGnPonaK6CF74PSdkw6sxuuZQtIYGs736Hsh/+iNb163vtZIvrJl5HYZJ2OkS6KtwewmwPYU90EdzTSuNLO3ANSiF1TiEJY9PVQtGLmaZJU20rpZvqGTgmHXeyiy0rqnj74U244u3kDvUyYkYuecVenHGRYjiv2GttaJF+ostj3gzD8AA20zSb9v76FeAXpmm++HnPGTd6lHn52CGMO34+s86/FHdySpcyxIxACzz5lciOcnb3DVw3w2ECu3f36hv1ROTI7d9C4V9djXtiFqkLhmKaJqG6Nhxpmk7QW7X6AmxeXrV3BnE9zXVtAMy7ahTDpubgb2zHV99GekEiNh3dLRIVVo15ywae3DtM3AE8+EXFMYAzLp5JJ53OypeeZePSd5h13iWMn3cKNnsff7vImQDn3RP5tWmCvxY8GVG/jGGzdRTHgYoKnDm9b6e+wldBe6idAckq4kU6o2lJKb6l5Qe0ULgnRGatG4ah4rgXMcMmtWXNlG6qx5vtZuDodAJtId56cCPuZFfHuLW8Yi9puZGbl93JLtzJLouTi4ilB4XU7NrBG3ffxs51qykcNZZzb/pN/zm1583fwfK74UuvQEpBt1yi9s67qL7lFoa88ALO7KxuucaR+uqrX6WutY6HT3vY6igivVq4PUTbpjriR6djGAZ1T5YQqGrZe5CHWih6G9M0Wf3aLko3RXaI2/xBAEYfk8+ci4YD0FDtJzkjof/8vBOxmGUHhRypjMKBnPPjX7H5w6UEAwEMwyAcDuGrqyMpPfo7q73KyNNg6S1w30K46kVwpx36OZ2UdMLxVP/lL1T/7W/k/ebXUV+/KzxOD7ubdlsdQ6RXMk2T9h2N+JdX4V9TjdkWIuvrE3AVJuE9cyiG3nrvFUKBMJU7GikrqSfYFmL6giEYhsHG9ysItIUYMjGTvGIvucVekvebHJKSqVPrRHo7y7ceDMOgeOrMjt+ve+MV3rj7v0xdcA5TTl+I0xVnYbpulD0aLngQ7l8ID10Ilz0VacGIIteAAaReeil77rqLtEsuJn7UqKiu3xUep0dj3kQOIlDlp/bejyItFC4bCWMycE/OxpmfCKDiuBf4eGk5Hy8tp2JbI6FAGICcwcmYpolhGCy8fjJOTZgQiWmWF8ifVjR+EoMnT+XdRx9g3RuvMueyqxl61Iy++VbUoKNh4W3w2JWw6Fo4796oHySS8ZUv07BoEZW/+z0D7r6r13wf3Q43vqDGvImE20O0rq8FG7jHZ+FIjceRkUDSnMK9B3mo0LJKe0uw41CO8i31nHbdeFzxDpr2tNLeGmLMMfnkFUf6iOMTPzmUQ8WxSOzrdQVyckYWp3/7BnbNO5nX776Np//0G8YdfxLzrr3O6mjdY/RZ4KuBpJxuOWXPnpxMxjeuo/pvfydQWoarID/q1zgSbqcbf8DfseMi0p8crIUirtiLe3wWhtNGxhXdN+VGDq10Ux1LHt9Mza4mTBNsNoOsoiT8je244h1MOaWIo04dZHVMEelGlt6kdyjhUIjVr75Aam4+ReMmEmhtJRQKEu9J7IGUFtmzDdKi+xevGQgQam7GkZoa1XW7YkPtBkrqSzh10KnYbdptkf6lblEJvg8qIi0UYzPxTM7CVZSi9oke5mtoi+wOl9RTtrmeo04dxJBJWVTvamLJYyXkFkcmTOQMSumYQywisedIbtLr1QXyp73z0D2sff1ljr7wcsbMOaHXnhJ3xLYvgXvPgNP+CpMujfryZjhM+/btxA0eHPW1ReTg9rVQ+JZXkrqwGEdaPG1bGwjWtZIwRi0UPSkYCOFw2mltDvDEH5ZTXxm5D8IRZyd3SAoTji9kwOh0i1OKSLTF3BSLzho2fTa7N6zn5Vv/zupXXuC4K68lb9hIq2NFT+FUGHQMPPMtSMyCYfOjunzlr39Dw7PPMvSlF7F7vVFdu7Ma2hrY2rCV4anDcTt1R7f0LftaKHzLKmlZW4PZFsKeFk+oPnKIR9zgFOLoJwckWcQ0TRqqWijbXE/ZpsixzbnFKcy7cjRxHgfZRcmMmpVHXrGXjAGJ2O19bMNFRLokpnaQIfKX3sdL3uLt+++kuW4Px15yFVNOXxjlhBZqa4K7T4PqjXDFs1DQqRc8X6h14ya2nXUWaZdeQvYPfhC1dY/E6ztf51tvfIuHT3uY0enqt5S+wQyFMew2Qs3tlP/mAwyHsbeFIhtXUbJaKLqRGTZprm8jae9BKU/9ZQWlG+sBSEhykjfUy6DxGQyfnmthShGxQp/fQYbIWLiRs+cwZMo03n/yUYomTAagtbkZZ3wcdofzECv0cnFJcPFjcMeJ8MC58LWlkRv4oiB++DC8Z5/NngcexHvBBcQNsu4mE48zcmqURr1JrAu3h2hZX4t/eSWYJpnXjMOe6CLjqtG4CpPVQtFNwmGT2t3NlJXUU7qpjvLNDYTDJlf/6WhsNoPh03IYOjmbvGIvqTlu3QwsIp0ScwXyPq74BI6+8PKO3796x7+o2raFuZdfw6CJ0dt1tURiFlzyBGx4GhKzo7p05re+SeNzz1H1pz9ReMstUV27M1QgS6xrL22meWnZAS0UnklZHZNZ4of2npti+4JQKEz1jiYyChNxOO188MxWlr+wA4DkjHiKxmeQN9SLGTbBZjByZp7FiUUklsVsgfxpo489nqptW1h0888YPOko5lx+Dak5MfwXZPoQmP2dyK9rt4AnE+KTu7ysIyOD9C9HZiOHGhuxJ3d9zSOxr+/YF9AsZIkdwbpWbB4nNpedtm0NtKypVgtFNwkFwlRsi8wgLiupp2JrA8H2MAu+O5H8YakUT8kmLc9D3lAvianxVscVkT7Gkh7kiRMnmitXroz6uqFggBUvPMPSxx8iHAxw6je/T/G0mYd+Ym/W7oO/T4TMEXDx4+BwdXnJcHs7BmC4ur7Wkar0VXLC4ydw04ybOHfYuZblEDmUcHuIlnU1+JdX0ralgdSzi/EclUO4PQQmaqGIkvbWIBVbG0j0xpOW56FiawNP/H45GJCen0hesZf8Yi8FI1KJc8d4K52I9KiYGfOWl5dn3nLLLcyaNYvs7Oi2EAA01+1h6eMPMuu8S3CneGlpaiQ+MSl2e9BWPQhPfRXGngtn3QZRGm8X9vtp377dkiOo20PtvLnrTUalj6IgqaDHry9yKGYwTN1Tmz/TQuGeko3Dqx3LrgqHTXauq430EJfUU72zCTNsMv74QmafW0woGGbnR3vIHZJCvEcFsYgcuZgpkIcNG2ZefvnlBAIBhg0bxnnnnYfD0T3dHmY4zEM/uR7Dbue4K64le/DQbrlOt3vnz/Daz2HGdTD/11FZctd119G6eg1DXnoRm1uj1kSCda0ESptJGJMBQPVtayKF8b4Wilh9kd0L+BvbKd9cTygUZthROZimyZ3XL6a9NUh2UXLkyOZiLzmDU3DF95nuPxHpBWKmQJ4yZYr59ttv8+GHH1JbW8vChZExbeXl5eTk5ET1h5AZDrPurVd558F7aGlqZNxx85l1waW4k2NsBqlpwgvfhw9ug4W3w7iutyX4V65kx4UXkfH1r5P5jZ4/yvuD8g9IiUtheNrwHr+2yD6fbqEwnDZyfzIdm8uuo9C7aPvaGravqaGspJ66isgNuen5Hi74yTQAasuaSclIwOFSm4qIdJ+YKpA/PQe5rq6Ov//972RmZjJ79mxGjx6N3R69vzRbfc2898RDrHjhGVwJCZzzo1+RM6Q4auv3iHAI3vs3HHU1OBOismTpd79L0+tvMOSlF3F2Q7vLF5n76FyOLTiWn838WY9eV2Qf/5pq6h4vwWwPdewUuydm4UhTC0VnmKZJU20rZSX1VG1v5OgLhmEYBq/fu4EtK6rIHert2CHOHJCE3aFDOUSk58R0gRwKhVi3bh2LFy+muroar9fLzJkzmThxIk5n9PrPanfv5MOnF3HCl76Gw+WitbmZ+MTEqK3fY1oboGYzFEzu0jLtu0vZesopJJ9yCnk3/zZK4Q7PaU+exqi0Ufz+2N/36HWl/wrWteJfURU5yW5QCoEqP01v7Y60UAxSC0VnVWxtYM0buynfXE9zXRsAcR4HF/x4GompcbT5AzjjHdg03UNELBTTB4XY7XbGjx/P2LFjKSkp4Z133uHFF19k+PDhpKSkRO2tzvSCAZz0tW8DEGhr5d4bvkHu0OEce8lVJGdmdXn9HvPsd2DTy3Dl85A77oiXcRXkk3b5ZbSsW4cZCGBE8cXIobgdbnxBjXmT7hVuD9Gytgb/ikgLBUDyvIHEDUrBmeUm7dxhFifs/cywSW2Zb+/ItTomzR9I1sBk/I3tlG6s69gdziv2kpbr6Rh3p2kTIhKrek2BvI/NZmP48OEMGzaMPXv2kJIS6RV+5JFHSEtLY/r06SRHaXavYdgYd9x83n/qMbau+JCpZ57DlDMW4nTFRWX9bjXvl7DzPXjgHLj6FUgdeMRLZX7zm+Bw9Pjumcfp0Rxk6VamaVL1j5UEq1uwp8WTPG8g7klZODQ397A017Xx1kMbKd9cT5s/CEBiahy+hnYAisZlMGh8hnbeRaTP6XUF8j6GYZCeng5AMBjE4XCwdOlS3n//fcaPH8+sWbM6Pn+kHC4X08++gFHHHsfb99/Fu489wLo3X+GCn/+epPSMaHwZ3SclHy5ZBHfOh/sXwlUvg+fIvh/7do0DFRUEq6pIGHfkO9Kd4XF6qPJX9ci1pH/Y10LRWlJH5jXjMOwGyScWYU90agrFFwgFwlTtaKS0pJ7yknpyh3qZckoR8R4HDdUtDJ6YSX6xl9xiL8npn9z/oNYJEemrek0P8uHYs2cP7777LitXriQUCnH++eczcuTIqOXa9dFaPl78Fidc83UMw6DN7yeut48/27EU7lsAxSfC+fd1aalt555HqKGBwc8+g60HDhH5eM/HhMIhRmeM7vZrSd/16SkUAHFDUkg7fwT2ZOsOw+nNzLDZ0Qbxwn/WsmN9LaFAGIC0PA8jZ+Yy4YQBVkYUEYmamL5JrzOam5v54IMPmDlzJvHx8WzduhWAQYMGRW2HqLluD/f839cYdcxxzDj3IuI9vfhGvs2vQubIyK5yFzS/8w67rrmWrBtuIP3KK6KTTaQbmKaJGQhjc9lpLamj5o512NPj8UzKVgvFQbS3BCnf8smxzcFAiPN/NBWAxY+VgAl5w7zkDk0hIVEvKkSkb+k3BfKn3XPPPWzbto28vDxmz57NiBEjsHXxtLmW5iaWPHwvq199kYTEJGZfeDlj5p6AzdaL53WGQ7BuEYw9B47whcLOa66lZdUqhrz8Eo7U1CgHPFBJXQmb6jZx6uBTu/U60ncE97TiX1GJb0UVCWPS8Z4yGDNs0r6zEddAtVDs0+oLEOeO3Ffw/tNbWf7Cdkwz0hKRVZREXnEq088c3LGLLCLSl/XbAjkQCLB69WqWLFlCXV0d6enpzJs3jxEjRnR57cptW3jj7lsp/fgjsgcXc/7Pb+69N/GtfRyeuBqOvQHm/vCIlmgrKWHrgrNIvfBCcn78oygHPNC/Vv2Lf6/+N6svW43N0FxU+Xz+1dX43i+nbWsDGBA3xEvi9NyOE+/6O19DG+WbGyjbVEfZ5npqS31c8svppGS62b62hsrtjZFT6gal4IzrxS/yRUS6QUyPeesKp9PJlClTmDRpEh999BGLFy+mrS0yk7O9vR3TNImLO7KiNnvQEM7/2e/4+N23qdq2paM4bm9twRUfncM6ombM2bD1DXjrd5CUA1Ou6vQSccXFpJ5/Pube71t37sh5nB4A/AE/ia5e3MIiPc4Mm7TvbiJuQGRiTevHewg2tGkKxV5Ne1pxuGwkJLrYtqaG5/+1BgBHnJ3cISkMnZzdcTpd0dgMisbqhYSISGdYsoOcVzzafP71JYwvSOmWAsw0TUzTxGazsWTJEt555x2mTZvG1KlT8Xg8XV6/avtWHv35D5i64FwmnXImjh6cHXxIoQA8fFGkL/m8+2DkaZ1eoqeO131s02P8YukvePWcV8n29OwpftI77d9CEdrTStY3J+LKSyTcFsRw2ftlC4VpmjRUt3T0D5dtqqdpTyuzzy1m/PGF+Bvb2fheBXnFXjIGJGK3690YEZH9xcwO8p7mdhb8cwmDMz2cPamABRPzyfdGbzfWMIyOH6RFRUXs2rWLt956iyVLljB58mRmzJiB1+s94vXj3B4KRo3lnQfvZt0bLzPn8msYPPGoKKXvIrsTzr0b7jkdnr4OBh0D8Z2bG73ve9eydh2EQySMH98NQcHjiLxY0WEhEqxtoe6JkgNaKJLnDcSREfl7wRbXJ97sOixm2GRPhY9ge5jsomQCbSEe/Nn7mGGT+EQnecVexp9QyMAxkbGO7mQXE0/UxAkRkWiyZAd54uTJ5o3/eZInVpTywbY9GAa8+t1jGZLZfW+zV1dXs2TJEtasWUNRURGXXXZZl9fcvmo5r9/zX+rKdlM8bSanf+cHvWeHy1cLddugoFMvmDqYoRBbTjoZm9vNoEVPYNij37f41q63uO7163jo1IcYkzEm6utL72WGTdq3N2AGTeKHpRJuC1H9n9UkjMnoly0UNbubKN1Y37FL3OoLkD/My4LvTgJg8/Iq0vI8pOa4e8/fMSIiMSImb9LbWevntY8ruWJmEYZh8LOn11Pvb+fsyQXMHJKBPcp3WTc0NNDW1kZWVhYNDQ288MILzJo1i8LCwiNaLxQMsPLFZzHDYY4642xM0yTY3oYzrhf9gF/zKBTNhuS8Tj2t8YUXKP3Od8n91S/xnnNO1GM1tjeyu2k3RclFuJ29fN60RMWnWyhcA5PJ+mr3vEPRW4VCYap3NLGn3MeoWZE/k0//bSW7NtSRnBG/37HNqaRk9rL7HEREYlBMFsif9pvnN/DwBztpbA2SnRzHgon5nDu5gKFZSVHPsXnzZp544glaWloYOHAgs2fPZujQoV3aodm87H1evf2fHHPxlYycPcf63Z7mavj7RPAOgCufhwTvYT/VNE12XHgR7aW7GfLCi9gTu96/Lf1X/XNbaX6ntKOFwjM5m/jR6dhcfX+qQm1ZM1tXVlNWUk/F1gaC7WEMA770l2NwxTuoLW3GleAgKa0XvbAWEekj+kSBDNAaCPH6x1UsWrGbNzZWc+n0gfzsjNGEwyZ1/nbSE6M3Zq2trY2VK1fy7rvv0tjYSG5uLldffTUOx5H1PFZu3cyrt/+Tii0l5A0byXFXfpnswUOjlveIbHkDHjgXCqfBJU+A8/B/CLesWsX2Cy4k/StfJuvb345qLF/Ax3Nbn2Ny9mSGeIdEdW2x1r4WCt/yKlJOKsKe5KLlo1oCFb5IC4W37xaCgbYQFVsaKNtcz5hj8vF441jzxm7eeXQT6fmJ5BV7I8c2D/Xi1kl/IiLdrs8UyPuraW4jHDbJSo7n/a21XHz7+8wZnsnCSQUcNyKLeGd0dp+CwSDr1q2jtraW448/HoCNGzcyePBgnJ2cUmGGw6x/6zXeeege/I0NTD3zHI6+8PKo5Dxiax6DRV+CUQvgnLugEweplP/kJlxFA0m/+uqoRqr2V3PcY8fx42k/5vwR50d1bbHGp1sojDg76RePJH5Y9x46Y7XmulbWvL6bss31VO9oIrz3KOdTvjqWorEZtLUEIzfZeXrRxBsRkX4iZqZYdEbGfrvFed4Erj56EE+tLOXVDVUkxzs4bXwe358/HK+7azsxDoeDCRMmdPy+pqaGhx56CI/Hw/Tp05kyZQoJCYfXD2jYbIyZO4/iaTNZ+vhDpBdE7jAPh0KYpon9CHenu2TcudBcAS//GLZeCkNPOOyn5v7yF90Sad8cZE2xiG37xgKGmtup+MOHQKSFImXewD7ZQtHS1E7Z5si4tdyhXoZOzsI0YfXru8guSmbiiQMih3IMScEVH/mzHpfQ6/+qFRGR/fT6HeSDCYVNlmyuYdGK3Xy4vY43r5+D025j6ZZaClITKEzr+g1fpmmyfft2Fi9ezJYtW3C5XBx11FHMmjULt/vI1l/x/P9Y89pLzL3iWgaOndDljEdk97IjmmxhmiZNL7+CsyCfhNGjoxLFNE3G3zuea8ZdwzcmfiMqa0rPMMMmbdsa8C+vxAyGSb9oJAC+FZXEDU7pcy0UZtjk7Uc2UbqpnrryyAs6h9PGpJMGctSpgwAItoc6DucQEZHeo0/uIB+M3WZwzLBMjhmWSTAUxmG3YZom339iNbv2tDB1UBpnT8rnlLG5JMUf2VuahmEwaNAgBg0aRHl5OYsXL2bZsmXMnj0biLRkdLZP2ZuTR7C9jcd/9WOKp83k2EuuJiWrhw/I2Fcc73wfGnbB2MObTmH6/VT88pe4Bgxg4AP3R+XmQ8MwcDvd+AP+Lq8lPeNgLRTuCZkdu8ieSbF94ItpmjTVtlJWUk9pST02A+ZeOhLDZlBb2kxSWhzDp2WTV5xK1sAk7I5PWpVUHIuI9B0xuYP8eXbX+fnfqjKeWL6brTU+4hw2bjhpBFfNHhSV9VtbW4mPj8c0Tf773/+SmprKrFmzyMs7/PFpwfZ2lj37JO8/9SiETeZeeS3jjj8pKvk65cHzI6ftXfTIYbdb1D36KBU3/ZT8v/6V5JPmRyXG8Y8ez+yC2fx85s+jsp5EX7gthGE3MBw2Gt/YRePL24kbuncKxajYbqHY/9TI5S9uZ91bpTTXRY6pj/M4GDgmnXlXjv7MY0VEJHb0yZv0joRpmqzaVc+iFaXMG5XNMcMy2Vbj48H3d7BwUgEjczt3stynBYNB3nzzTT788EPa2toYMmQIs2fPpqio6LB/gDbV1vDW/Xcyft7JFI4aSygYwGZ39NwP4NZGuOsU2LMVrngW8icd8ilmKMS2sxYS9vsZ/Nyz2OK6Pk1kV+MuEl2JpMb37Zu4Ys3+LRQt62pIPXsY7vGZhHwBzEAYhzd6k2R6khk2qS3zdRzIUbmtgQt/Og1XvINVr+6kcltjxxzitFwPRpTnsIuISM9TgfwFnlpZyvWPryYQMhmVm8zCSfmcMSGPrKQj75VsbW3lww8/5L333sPn83HeeecxatSoI1rrjbtvo3rndo674loyBhQdcaZOaaqA2+dBsAWufhnSBh/yKb5332XnVVeTdf33oj7VQqxnBsM0vrEL/4pKQnVtkRaK8ZkkzszDmRN7c7DDoTCmCXaHja2rqnn93g20+YMAJKbGkTfMy8yzhuKJ0YJfREQOTQXyIezxtfPM6jIWrdjN6t0NJDjtLP/JCbhdji69fRoIBFizZg3jx4/H4XCwdu1agsEgY8eOPew+5TWvvsg7D91Dm9/HhBNPZea5FxOf2H1Hb3eoKYE7ToTxF8BJvz2sp5Tf9FM8M2eQfFLXW0Ne2fEKvoCPBUMXdHktOTLhthCBCh9xA5MxTZPKv67AnuyKyRaKUCBM1Y5GSkvqKS+pp3xLA8ddNpKhk7OoLW1m9eu7IjvEQ70kZ+iUOhGR/kAFcidsrmpiXWkjCybmA3D5nR+QmxLPwkkFHFWU2qVWhwcffJBNmzaRnJzMjBkzmDRpEnGH0Y7Q0tTIkkcfYM0rLxCXmMgp1/0fgyZMPuIch612C6QWga3nC6FvvP4NypvLefyMx3v82v3ZAS0Ua2vAZpD342kYTjtmIIzhPPw52VYKtIdobwniSYnDV9/GfT9ZSigQBiAtz0PeUC8jZ+WSNbBrbVUiIhK7+s0Ui2gYmpXUcXx1IBQmIzGOp1eX8fCHuyhMS2DhxALOmVxwRCPjLrzwQjZv3szixYt56aWXeOutt5g/fz4TJ078wuclJCVzwtVfZdzx83nr/jvxZucAEAoGu3d2cvreU+waSmHJ32D+r8H+xdM/wu3t1N13P4nHHkPc0CM/KdDj9OALaA5yT2r5eA/1T20mVL+3hWJiFu7J2bB3IkNvLo7bW4OUb2mI9BBvqqdqRyPFU7I54cpRuFNcTDi+kKyByeQOTSEhSafUiYjIkem3BfL+nHYbfzpvPL84czQvra9g0YpS/v56CZlJcVwyfSD+9iCBkElKwuGNjDMMg+LiYoqLi9m1axeLFy/umJ3s9/tpb2/H6/V+7vOzigZz7o9/1fH7Z/5yM674eI6++AqS0jK69LV+oe2L4YNboa0RFvwbvmAXPezzUfOf/+D74H0G3HrrEV/S4/DgD2rMW3cKtwVpWVuDMy8RV14i9kQnjswEUk4q6vUtFK2+APVVfnIGpQDwxO+Xs6fMh81mkDkwiQknFDJgVDoQ+XM3fYGOLBcRka5TgbwfT5yDhZMKWDipgPKGlo4ZyotWlPKLZz9i3qhszp6Uz9HFmTjth7fLVlhYyIUXXtjx+3fffZd3332XsWPHMmvWLLKysr7w+eFwiMwBA/nwmUVs/vA9pi08n8mnLsDRyeOvD8v486FuO7z5G0jKhRN++rkPdaSmkvHVr1L1+9/TvHgJibNnHdEltYPcPcywSdvWBvwrIi0UZiBM0rEFuPIScRUkkXn1WKsjHpS/sb1jwkRZSR21pT7i3A6u/uPRGDaD6WcOxuGykzM4BWdc7y3sRUQktvXbHuTO2FTZxIPv7+Tp1WXs8bWTkejijPH5/OjUkdg7OQaqvr6epUuXsmLFCgKBACNGjGD27NkUFBR88fMqK3jz3tvZsuw9vNm5nP7dH5BVdOipE51mmvDsd2D5XXDyH2DatZ/70HB7O1tPPQ1bfByDnnwS4wjaQP6z+j/8c9U/WXnpShw2vV6LBtM0qbplFYHS5o4pFO7J2bgGJPW6Ob5NeyKHcgyZlInDaWfpk5tZ8dJOHHF2cgcnk1ec2nFss00j10RE5AjoJr1uFgiFeWtjNYtW7qbOF+Cha6cD8NL6CiYUeslOPvyRcT6fjw8++ID333+fwYMHc9555wGHPoxg+6rlvPfkIyy4/ibiExMJh0LY7FHeSQuH4JFLoX4nXPM6OD6/l7PxpZcp/da3yPn5z0k9/7xOX8oX8BEMB0l2Jfe64i1W7GuhaC2pJ+384Rg2g+b3y7HF2UkYnY7h7D07rS1N7WxbU0P53pPqmmpbATjr/yaSV5xKQ7Wf1uYgGQMSsR/muzQiIiJfRAVyDwqHTWw2g6bWAJN/+SrBcJhZQzM4e1IBJ47Oxu06vN3QtrY22traSE5Oprq6mieeeIJZs2YxatQo7IcofMPhEA/9+HsUjBrL9IUXEOfu/A2FnyvQAqF2iE/5woeZpknlL39F8umn4T7ETYgSPZ+eQmEGwjgyEsi8Ziz2lN4x09c0TerK/ZSV1JFVlEzWwGTKtzSw6A/LiU90doxbyxvmJT0/UTvEIiLSLVQgW2RbjY8nV+zmiRWllNa34HHZ+dN5EzhpTE6n1tmxYwfPPPMMNTU1HcdYjx8/Hufn9Bu3t7bw+l23sv7NV/F4Uznm4isZOXsOhi2KO2+BlkjLxcxvQPbo6K2719b6rfxvy/+4eOTFZLm/uB9bIoWxYTNo+XgPtXevx4i34x7Xe1ooQsEw694qpWxzpI+4tTkAwJRTiph2xmBCwTANVS2k5rotzyoiIv2DCmSLhcMmH2zfw6IVu/nanKEUZXhYsrmGpVtqOWtSPkMyD33wRzgcZuPGjSxevJjS0lK8Xi/f+MY3vnA3uXzzRl6/61YqNm8id9gIzvjOD0hMS4/OF9VQCrcfDxiR0/a8hQd9WLCujpp//ou0K67AVZB/2Mu/s/sdvvba17j/lPsZnzk+Opn7mHBbkJY1NfiWVxI3xEvKvIGYoTAt62pJGJVmWQtFKBSmekcTZSX1OFw2xs0txDRN7rx+Ma54e8fucF5x5FAOFcQiImIFzUG2mM1mMH1wOtMHf1KcrthRx7/e3Mwtb2xmQqGXsycXcPq4XLzug/f12mw2Ro4cyYgRI9i+fTs1NTXY7XZM0+SDDz5g1KhRJCUlHfCc3KHDueiXf2T926/z0duvk5AcaYsww+Gu7yan5MMlT8CdJ8H9Z8NVL4I77TMPM1tbqX/8cUJ79pD/5z8d9vIeZ+T4Yk2y+Ky2rfX4PqykZd0nLRT2lMj/N4bdhnt8piW51r1dypYVVVRsbSDYHjmUY8DodMbNLcQwDC7++XTiPd0wZUVERKSHaAe5B1Q2tvK/VaU8sbyUjZVNDM708Np3j8UwjMM+4rqqqop///vf2Gw2Jk6cyMyZM0lL+2yhuk+b38+DP/4/xp9wEuNPPLXrB41sewfuXwh5k+Cyp8D52WN6q//+d2r+9W8GPvTgYfcjf7znY8595lz+MucvnDDwhK5l7ANCDW0dPcS1939Ea0m9ZVMoAm0hKrZGDuWo2d3MKV8di2EYvH7fBqp2NH3SQ1zsxZ2sQzlERKR3UotFL2eaJh+VN1Ld1Mac4Vm0B8Oc/Le3mT00g4WTChhXkPKFBVBtbS3vvvsuq1atIhwOM3r0aObPn/+ZHWWApj01vPTvv7FjzUrSCwYw9/JrGThuQte+gHWL4Pnr4YpnIWvkZz4d9vnYctLJOPPyGPjwQ4dVzO1q3MUpT57Cr2b9ijOHntm1fDFq/xaK9u2N5HxvCo6MBEINbdjcjh5vodi+poZlL2ynekcT4b09z5mFiZz+jQnEJzo7+qBFRERigVosejnDMBid98lUiMbWACNzk3now13cs3QHQzI9LJxUwLlTCshK+uzIuPT0dE4//XTmzJnDe++9x0cffURcXGS30efz4XZ/cuNTUloGZ//wF2xZ/gFv3vtfHv/1jymeOpOTr/suzrjDH0d3gDELYegJEJ980E/bPB4yv/1tyn/0Ixqff56UU0895JJu594TBvvhaXrB+jYaX9r+SQtFZgLJJxVhJET+WHb3NIqW5nbKSyI7xKUldRx70fCOE+tsNoOJJw7omEHsiv/krwoVxyIi0tdpB7kXaGgJ8Pzachat2M2H2+t45NrpTBucTm1zG/FOO564g7+OCYfD2Gw2QqEQt9xyCx6Ph9mzZzNs2DBs+/UeB9vbWfbsk1Ru3cwZ//fDSGtHV/qTTRPe/C3YnHDs9Qd+KhSi6s9/JvWCC3AVHvyGvgOXMgmEA7js/eMt+mBNC+GWIK7CJML+ABV/Xk7C6PRIC0Vh97ZQ7BtNWF/l5/l/r6WuPNL3bXfayBmczLTTB5M71Ntt1xcREbGCWiz6gJ21fgpSE7DZDH729Hoe+XAXJ4/J4ezJBUwfnH7Qk/tCoRArVqxgyZIl1NfXk5mZyaxZsxg7duwB0y/29Ts3Vlfx+G9uYtZ5lzBs+qzOF2WmCU9+BdY8DGfcApMu7eqX3aeFWyMHeexroXANTCbrq5GJHWbIxLB3T1HcWNMSGbe2KTJybcjkLGYsGEKwPcSLt60jd2gKecWpZA1Mwu7QoRwiItI3qcWiDxiQ/slhH2dOyKMtGOLZNeUsWllKbko8l0wfyNfnDj3gOXa7naOOOopJkybx0UcfsXjxYp566ini4+MZMWJEx+P2FcJtfh8Op5Nn/3ozhaPGMvfKL5M5oOjwQxoGnHkL+KrgmW9BYhYMm3/AQ9p37qTqj38i56af4MjI+MLl/rr8rwzxDuH0IacffoYY0fjaTpre3HVAC4Vn4ifznqNVHJumSasvQEKiC9M0eeRXH1Jb2gxAnNtBXrGXjILImEGHy85p12mknoiIyOfRDnIMaA2EeHVDJYtWlJKTEs9vzhqLaZo8vnw3x4/MJs1zYHuCaZps3bqVQYMGYbPZWLp0KW1tbUydOhX33tP2wuEQa197icUP30ebz8eEk05l7uXXdm43ua0J7j4NqjdGbtwr+OTFWdvWbWw94wy8Z59N7s9/9oXLzHt8HtNypvGr2b86/Gv3UsGaFnwrKkmanY/N7cS3opL2HY1Rb6EwwyZ7yn2U7t0dLttcT0KikwtvmgbA8he344xzkD/MS1quR33DIiLSb2kHuY+Kd9o5bVwep43LY98Lmo2VTVz/+BocNoO5I7I4e1I+c0dkEeewYxgGQ4YM6Xh+ZWUlq1atYsmSJUyePJkZM2aQkpLC+HmnMGzG0Sx55H7CoXBH8Xa4o+eIS4KLH4O7ToY92w4okOMGDyL1wgupe+ABUi+6iPjhwz53GY/DE9M36X26hQIDXAVJJIxKxzMpG8+k7K5fIxSmttRHRmEihmHwxgMfs2FJOQCJqXEUjkwlvzi147/d5JOKunxNERGR/ko7yDHs44pGFq0o5cmVpVQ3tZGS4OS+q6cyrsD7mcdWVVWxePFi1q5di2EYzJ8/n2nTpnV8fl9hVbbpY167898cd8WXyR8x6vCCBNvBsXcXOxyGvTf/herr2Tz/JBJGj6bwjts/t+i++LmLSXQlcuu8Wzv19fcGoeZ2Kn73YUcLhXtyNp6JWV2eQBEKhqna0URZSR1lJfWUb2kg0Brikl/OICUzgdJNdTTtaSVvaOSUOhERETk47SD3MyNykvnhKcl8f/5wlmyp5elVZQzLjsxEfnTZLiobWjlrUj4FqW6ysrJYuHAhxx13HO+++y55eXkA1NfX09zcTEFBAQDtrS34Gxt4+KffZ8SsYznmkitJSvviHuKO4njDs7Dkb5GT9+KTsXu9ZH7tq1T+9mZ877xD4jHHHPTpbqc7Zk7SC9S04F9eidkWwnvGEOyJLpKOH0Dc4JQutVAE2kNUbmvEm5VAYmo8W1dV8/Lt6wFIzfUwfGoOecVeEhIjJ9TlD0uN2tckIiIiB1KB3Ac47DaOHZbJscM+OXp4+fY6Hlm2iz+9sonpg9NYOKmAU8bm4vV6OeWUUzoet3TpUt5//32KioqYPXs2Q8ZO4Ko//4cP/vcYHz6ziC3L3mfW+Zcy+dTDOMTDEQ9lK+CRS+Dix8HhIvXCCwm3tJLwBSfrJbuSaQm2dOl70J3Crfsd5LEj0kIRPzK9Y9c9ec6hx9l9WigYpnRjHaUl9ZSX1FO5vZFwyGT2ucWMP76QwhFpnPzlseQOTSEhqX+MwBMREekt1GLRh+3a4+eplaUsWlnKthof80Zl89/LIu8w7JuJ29bWxvLly1m6dClNTU3k5ORwzDHHMGrUKOorK3jrvtvJLR7B1DPP6eh//sJd0lUPwlNfhTHnwML/drRbxBozvPdrtRk0vLKDptd2dqmFotUXoHxzPXanjQGj0mlvDXL7d98BIGtgUuTY5mIvuUNSiHM7o/71iIiI9FeagywHZZomK3fVYzcMxhd6Katv4ex/v8sZ4/NYOKmA4TlJBINB1qxZw5IlSxg4cCBnnHEGAMFgELs9cuPfx+++zfq3XmPu5deQllfw+Rd850/w2i9gxnUw/9cAtKxaRdVf/krBLf/AfpCjsXuLfS0U/hVVeM8cQsKodEINbYQa23EWJHaqhWLb6mp2bYj0ENeWNYMJhSNTOeNbkd30iq0NpOV5DjilTkRERKJLPchyUIZhMGnAJz2r/vYQo/NSuGPxNm59eyuj85L3HnE9lgkTJtDe3g7Arl27eOSRR5g+fTpTpkwh2N5O2cYN3PO9rzPplDOZvvAC4tzuz15w9nehsRzCwcihIoYBTif+Dz6g5j//Ifv6A0/fe2XHK7yy4xV+f8zvu/X78HnMUBj/8qoDWyiGpWJzf3Lk86F2jJv2tFJWUk9jTQtHnToIgLVv7qZ8SwM5g1OYdvog8oq9ZBV9ckx3zuCUz1tORERELKQd5H6strmNZ1aXsWhlKevLGln6g+PISopnd52fjMQ46mqqeOWVV9i6dStxcXEcddRRjBs5gpXPPMG6N1/FnZzC8Vd/lWHTZn128XA4UhgbRseUi7If/JDGZ59l8PPPHXAM9W1rbuMfK//BiktW4LT3THuBGTYJ7mnFmZGAGTap+MOHGA4bninZuCdmYU8+dAvF7o11bFxaTtnmehprWoHIoRxX3DwLh8uOr6GN+EQndntstpmIiIj0BdpBlk5JT4zjilmDuGLWIMrqW8hKigfghifWsGZ3A6eNy+PsY07j+ONbWLJkCYsXL2b16tV8+9vfZvwJJ/P6XbdihsPAQWYn7+s9rt4ED5wDZ/ydzG9/m8YXX6TqT3+m4K9/6Xiox+kBwBfw4bV7u/VrDlT78a+owr+iCjMYIvcH0zAcNrK+NgFbovOgLRSmaVJX4Y8cyFFSz8yFQ0hMjWdPWTPb19WSV+xl3NxC8oq9pBckYtt7KIeni6PeRERExBoqkAWAPO8ns3S/Pmcojy/fzVMrS3nog50MSHPztTnTue6446ipqcFut5M1eCjpR88juShy7PWHTz9BXXkZR194Ge4U7ycLJ2aBywMPX4LzyudJ/9LV1PzjFlpWX0HC+Mhxx25HpE3DF/ThZb/nRlHb1noaXtpxQAuFe3I27K2H7QeZFFFX4eO9/22lfHM9LU2BSNYUF421rSSmxjP66HzGzimI2ul4IiIi0juoQJbPmDk0g5lDM/jlgiAvrqtg0crd+NpDZGRkkJDk5aEPdjIt18HyFStY+t57FBcX4w20sPHt19n03mJmnnsxE+afit3hgARvZOTbHfPggXNIv+gZnNnZxI8e3XG9/XeQo8UMm7RtqceeGo8zIwEwCLcESDl5EO6JmQe0UIRCYap3NnXsEA+dlMWIGbk4XHaqdzYxcHQ6uXunTKRkJnQUxHaHWidERET6IvUgy2HZ10Lx3Jpyvv7gClwOG/OHpzLZvYeqLevw+/3kZGfh3VNB6ZoVpOUXcuKXv0n+8JGRBao+hjvngycDrnoZPJ/MEX6//H1++M4P+cfx/2BU+mGe3vc5PmmhqCTU0E7i7Hy8pw0+YETdvuuGQ2Ge++cayrY0EGwLAeDNdjPhhEJGH53fpRwiIiLSO6gHWbrNvl3TU8bm8L+vz2LRit08vbqMZ/wmWZ7x3Hx8Eju3bOLcG3/K9lXLeOX+uzngpVfWCLjoEVj8F7A7aXzlFWr/cysD77+PabnTeO2817qUzzRNau5aT9umuo4WipRTB5MwMp1AW4iKrQ0dO8RxbgenfHUcNrsNV4KDkdNzyBuWSl6xF3eyDuUQERHp77SDLEesPRjmzY1VvL9tDz85LbLz+9dXN+G2G9R9+CQup5OZM2fSuH4lbo+HqWeeizM+ciOg79132HnVtWR++1tkfOUrnb72vhaK1pI6Uk4ehGEYNL62E8Nhwzk6nfiMSE/1Ww9u5KPFZYTDJoYBmQOSGDA6nWlnDI7eN0JERER6LR0UIpYyTZNL7nifJZtrKLQ3MCuxhvi2OhwG2KpKSSXE3IuvYPhRUzHuOZ3dL7TRvK2ZjKcf5acb/8IFwy/g6IKjv/Aan26hMOIdpFw7hqrKyBzi0pI66sr9XP2no3HG2floSRkN1S3kF3vJGZyCK0FvmoiIiPQnarEQSxmGwQNfms6W6maeXFHKkytLCbRVcVp2I0ETbK2NPPe337N65BhOHD+VrKJ/0/RxLs3/vI23R7zNzLyZX7h+68Y91Ny1HgxwDfWScupgtte38dQvPgTA7rSRMziZSfMHEAqGccbZGTUrrye+dBEREelDolIgG4ZxEvA3wA7cbprmzdFYV2LTkMxEvjd/ON+dN4z3ttVS4HXjNv18VBPittsforVxGy1NR3Ha1EtI2/wke556huxr7QdMsTDDJm2b6/EtryScFk9tShzlH9dh2GxsrmtjzoRsssZlklvhY/qCweQN9ZI1MBm7U5MlREREpGu6XCAbhmEH/gnMA3YDHxqG8bRpmh91dW2JbTabwcwhGXt/58bdvAdj5AxWbYujZcsW/mGkkTzyLMbkrKQurQlfwEd7lY+6d8oIbqjFbA5AvJ2P6topaQsT53aQO9TL5LmFZA1MAiA1x8PkkzzWfZEiIiLS50RjB3kqsNk0za0AhmE8DJwJqECWA0wpSuO+q6dR0TCeRR9sZuUH70E4zNLc4zlzeTmBj218FF5BOia+RBcDLhpB/Ig0Gt6vYNKgFNLzPBg2HcohIiIi3SsaBXI+sGu/3+8Gpn36QYZhXAtcCzBgwIAoXFZiUTgUxlbfzknpWVx5zkIqlu5kfclatjZWEKh8hbdSa2gfOJZjTjmahLEZGIahmcQiIiLSo6JRIB9sS+8zozFM07wNuA0iUyyicF2JETW7m9mxroayknpqtzQwAJMBcTZqDQNXgoOJwyczdkw2q/7zMzZmV+Fv+4hHntjCP14o4rJTj+XEsbrRTkRERHpONArk3UDhfr8vAMqisK7EoGB7iMptjZRtrmfiiQNwOO2UvFvGxjd348r2MGRiJkUb9+AclEzy9FwSRqZjOGyY5kh45r8Uv/kWgYuG84JzLslNG/ngf1vxtswje8holu+o46QxObhdGr4iIiIi3ScalcaHQLFhGIOAUuAC4KIorCsxoqHaz4Yl5ZRtrqdyeyPhoAkGFKa4cO5qonB9DYPHp5P95fEAhFuC2D41j/gvK/5C+PRsTl25npz3VvGVE4I8VDGEGhx8+OJzhEa38+cP6/nlUybHjRnA2ZPymT44HZt6kkVERCTKulwgm6YZNAzjOuAlImPe7jRNc32Xk0mv1OoLUL6lgbJNdQwan0lesRd/QzsrXt5J1sAkxs8tJJ8wzo/rCD67lVCCA89ROXgmZ3es8eniGGB30262JOziorMXUvf00wwtXcK1U3NY7TmDJY89SOjjVfx4yrHsampmy/rdXLsym6z0NF757rHYVSSLiIhIFEXlvWrTNJ8Hno/GWtL7BNpCLH1qC2Wb6qktawYT7A4byRkJ5BV7ycxxc/FFw0g6KgdbnJ2mxaW0NQVwT87qaKE4FLfDjS/gI+vb3yb98stx1L4GGcVMGno8I2YdyzsP3Uvpjm1Mmn4s9tVrGBpfRbyniJrqKrKzs/n+46sZk5/C6ePySPW4euC7IiIiIn2VmjnlAM11rZRuqqdscz2elDimnjYIh9PG9tU1pGQlMPW0QeQP85I5IInQjiZqH/qYlvU1EDRxprhwj80kaXY+SbM7N3nC4/TgD/hxZGTgyMiA4mLCLS3YAHewlvlf+SbB9nYcLhczpk7l0dtvpaF2Fw888ABXf+XrrC1t5NFlu/nlsx8xd3gWCycVcNyILFyHUZyLiIiI7E8FsgCw9KktbF5WSWNNKwCueDvDpuYAYNgMLv3VjI4ZxKHmdir/tJxwYzs29yctFM78xCO+vsfpwRf0YZomhmFQ+dvf4l+2nKLfXIPx8AWw4D84xp+/9/pNOHZvJa6xkQEzjsHR7ueZr8/grvsfpsKZw9Pb6nj5o0p+f844zptSSDAUxm4zMAy1YoiIiMihqUDuR0zTpK7CT1lJPWUl9dRV+Djvh0dhGAbhYJiMgiTGzS0kr9hLekFixw1wYX8A/5oawi0BkucOwJ7owj0mA9egFBJGph1WC8WhFCYVMj5zPMFwEKfdSfyYMey5514a1jXhHTgL/vc18GTA0OPJLR7OVX+9laVPPMyK55/mzhXvM/a0hTTXVRNq2MwVmVlkHDWO+aOyALjvvR3c994Ozp5UwIKJ+eR7E7qcV0RERPouwzR7fiTxlClTzGXLlvX4dfsbMxz5b2vYDDa8W8bSJ7fQ0hQAwJ3iIr/Yy5xLRuCK/+zrJDNs0lZSh295JS0f1ULQxFWYRObXxvfITqwZDrP9/AsIVlUx5KmHsT18NtRthyuehbyJHY/bU7abN+75L3aHk9O/+wPWrVvH4sWLqa6uxuv1ctVVV/HB7hZue2crH2zbA8CMwemcPbmAsyfla1dZRESkjzMMY7lpmlM68xztIPchoVCYmp3Ne3eI6yjf0sBp3xhPzqAUEr3xDBidTl6xl7xiLymZCV9YHDa+uoOm13d9poWipwpKw2Yj+8Yb2HHxJdQ+8ASZlz0Od5wID5wLX/8A3GkApOUVsPDGnxFsb8NutzMgK4OC1npmnHwyuyoqSEpK4oRRyQyO9xGOH87zG2pZtGI3jy3bxTmTCwBYV9rAyNxkTcMQERERQAVyTAsFwgQDIeLcTqp3NbHojysItoUA8Ga7GTIpC2ecHYDCUWkUjko76DrhliD+NdX4l1eSfOJA4oem4p6UjTM3MWotFIfyYcWH/Pq9X/PHY//I0NShALgnTybppJOof+QR0q+9Btuli2DLGx3F8T6GYeCMiwegeud2dqxeybaVy5hy2kKCbW2YNhuPPPIIpmkyZcoUnv7ydEL2yONrm9tY8M8lpCe6WDAxn7MnFTAsO6nbv14RERHpvdRiEUMCbSEqtjVQtinSQ1y5rZEJJxQyfcEQAu0hlj6xmdy9O8SelLgvXOtgLRSObDcppwwiYfjBC+nutLRsKde+ci13n3Q3k7Mnd3w8UFmF4XTgSPtUpqoNkFIIcZ+9MbBpTw3vPHA3Gxa/SWJ6BnMu/RIpg4ayZMkS1q1bh81mY/z48RxzzDEkJCbx2oYqFq3YzRsbqwmFTcbmp/DLBWOYUOjt5q9aREREuptaLPqYtpYgvro20vI8mKbJfT9+l5amAIYBGYVJjJmTz4DR6QA4XXaOuXD4IdcM+wPY3E4wYc9jmyBskjg1F/fkbJx5Hst6cj1ODwC+gO+AjzuzIzfameEw4cZG7F4vtNTDnSdBwVFw4UNgdx7wnKS0DE75xvcYN+9k3rjrNso2bWD4jNmcffbZzJ07l6VLl7Jy5UqOOuoovF4v80dlccrYXGqa23hmdRmLVpSSvneW8rLte6hqauO4EVnEO+3d/n0QERER66lA7kVamtsp37x3h3hzPTW7mkjN9XDhTdMwDIMZZw3BnRxH7pAUXAc5je7zRKZQVONfXkWosY2cG6Zi2A0yvzQWR0ZCj7RQHMq+Atkf8B/087u/9nXCfj8D7rkbI8EL834Oz3wLnv4mLPgXHKSwLxgxmot/+2dCwSAAu9avYePSxRx3/iUcd9xxJCREpln873//o7m5mdmzZ3PFzEFcOWtQxxoPfbCLJ1bsJjnewWnj8zh7Uj6TBqTq5j4REZE+TAWyhXwNbVRubWTQhAwMw+CdR0oo+bASu9NGzuBkppxSRN6w1I7Hj5yZ16n120ubaXpr1wEtFImz8yFkgs3AmeOJ9pd0xD5vB3mfxGOPoeLnv6D59ddJOv54mHwFNFXAm7+F5Fw4/qaDPs9ms2NzRXZ+K7duZs2rL7Jx6TvMOv9Sxp0wH5vNTm5uLkuWLOHee+8lLy+P2bNnM2LECGw2G78/ZxwLJubxxPLdLFqxmwff38kxwzK596qp3fJ9EBEREeupB7kH+Rvb2fVRLaV75xA3VLUAcOmvZpCckUD1ziaC7SGyBiZjdx7Zrm6gyo8tzo49JY6WjXuoe2Qj7glZlrdQHIov4OM7b3yHi0ZexJzCOZ/5vBkMsvXMBRAMMviZpzFcLjDNyC7yinvg/Adg5GmHvE71zu28cdet7PpoLZkDB3HcVV+hYMRoAoEAa9asYcmSJezZs4c5c+YwZ86BOZrbgrywthyn3caCifm0BUN85b7lnDQmh5PH5pIc7zz4RUVERMQyR9KDrAK5m5imSUNVC2Ul9eQPTyUlM4GSZZW8fPt64twOcod6O0auZRYmYrMfeZvDvhYK3/IqAruaSDq2gJSTB0XmIIfNXtFCEQ3Nb7/Nrmu/TPYPf0DaZZdFPhgKwoe3w5SrwOE6rHVM06Tk/SW8ed8dTDntLCadfEbH58LhMBs2bKCgoICUlBR27NhBaWkpkydPJi7uwBsft1Q3c809y9ha4yPOYWP+6BwWTspn9tAMHF347ykiIiLRowLZYu2tQTa+V9FxUp2/sR2AYy4Yxtg5BbS1BGmqbSU9z9NxbHNXmKZJ3eMl+FdXQdDEmePGPTkb94Qs7EmHVyzGEtM02fWlawjV11P0+GOf3Q331UDdDiiYfPAFPiXQ1orN7sDucLBh8Zs0VFUy5bSzcLg++d698sorLFmyhPj4eKZOncq0adPweD5pTTFNk9W7G3hi+W6eWVNGvT/Aoq/NZNKAVNqCIeIcurFPRETESiqQe1A4bFKzq4mykno83jiKp2TT3hrk9u+8jTsljrxiL/nDIjvE3mx31FobApU+WkvqSZqdD0Dd/zZjGEavb6E4HBc8ewFTc6by3Snf/dzHBKursaWkYHMd5AXAgxfAznfhyhche1Snrv3q7f9k9SsvkJKVzZzLrmHIlGkd38vdu3ezePFiPv74YxwOB7Nnz/5M+wVAWzDEks01zB2ehWEY/OjJtazYWc/Zk/I5Y0IeWUnxncokIiIiXacCuQesfn0XO9fvoXxLPYHWyKEcw6ZmM++q0QA017Xh8bqiWqh+uoUCm0HO94/C4f3iWcex5uQnTmZ81nhuPvrmQz423NpKuLkZR0bGJx+s3wm3zwPDBl96BVIKOnX9HWtX8cbdt1G7eycDx01k7hXXkp5f2PH56upqlixZQlZWFjNnziQUClFbW0tWVtZB13ts2S7uf38nq3fVY7cZHF2cwUVTB3Di6JxO5RIREZEjpznIURRsD1G5rZGyzfX4GtqZc1FkxvD2NTX46tsYdlQ2ecO85A1NJTH1k0J1/19HQ+vmOmruWg+hSAtFyqmDcU/I7JMtFB6n53OnWOzPDIXYfu65OAcMpPCft3zyCe8AuOQJuOtkuP9suOpFSEj9/IU+ZeDYCVz6u7+z+pXneffRB6ivKDugQM7MzGTBggUdv1+/fj2LFi1i2LBhzJ49mwEDBhyw3rlTCjl3SiGbq5p5cuVunlxRylubqjlxdA6mabJiZz0TC73YdMS1iIhIr6Id5E8p+bCStW/tpnJ7I+GgCQZkFiZx9g2TsdtthIJh7N1401ug0odvRRXObDeeSdmEW4M0vrIjcvRzjLdQHMrlL1yOw+bgjvl3HPKxNbf9l+o//5kBd9+NZ/q0Az+57e1IgTzmbDjrP0eUpbW5mThP5Pu9/LmniHN7GH3s8Ri2T/7b+/1+PvjgA95//31aWloYMGAAs2fPpri4+KD/ncJhE197kKR4J8t31HH2v9+lMC2BsyYWsHBiPkUZvWfsnoiISF+hFotOaPUFKN/S0HFD3clfHkNiajzr3i7l46Xl5O2dMpE7NIU4d/eO7wr7A/hXV+NbXklgdzPYDBKPzsd78qBDP7kP+eqrX6WutY6HT3v4kI8Nt7Wx9eRTsKWkMOjxxzDsn7oZruRVyJsAnoyDPv9wmabJ47/6ETvXrSFnSDHHXfkVcosPPLGwvb2dFStW8O677+Jyufja176GzfbFL6L87UFeWl/BohX/3959h0dVpwsc/54pmWTSG6lACD0ESKGFRLqALAgGRUBUcHHV1V3rFr3XLa7eu+u6eq93d5XFAtIEBaRKkxpKKKH3FkpIJb1Mkpk5948JiGyElElmSN7P8+RxZpzz+/2eJyfDO7/znvfNIOVcHqoK8e19+Z9HY2jrZ2zUmoUQQgjxPQmQ70BVVRRFITu9mC3zT3E9oxRU0OgUgiK8GDS5KwHhHs2+HoDcT45Sea6wpgpFMMbYQLQeLS+F4m7mHJtDfmU+r8T/+E16typas4Zrr75GyDvv4DMxufY3Warh2FLo9Wit3fbqQrVaOZmyle0LPqessIAeg0dw39Qncff5YfqGxWKhqKgIPz8/KisrmTNnDrGxscTGxqLX//iXrMyiCr45eI1NJ7NZ+HR/DDot645lotNoGNw1EL2UjBNCCCEaTALkW5QWVHLtbMHNHeJeQ8OJHhxO8fUKtsw7dbMGcVCEFzqX5ivFVZ1dRtmBHCqO5NLmhRi0Hi5UXi5G0WpafAqFvamqyqXJU9CFhBD+Px/U/qa0L2DlL2DYmzDotUbNV1VRzp7lSzi4diVT3n6PNhGRP/re69evs2zZMjIyMjAajQwYMIC+ffvebG99N8n/3Ena5UL83V14MCaUiXHh9Aj1kvNDCCGEqKdWGyCrqkp1pQUXVx2WaiuL3kqlKNfWpc7FVUtIJx96DAqjQ6/GXW5vKKvJTPnBnB+kULh288NnTAd0AXULmETtLIWFaLy9fzxwtFrhm2fhyGIY/w+IndboOStKinHz9AJg5+J5hHWNIiLm32svq6rKpUuXSElJ4dy5c7i4uPDCCy/g5eV11zmqLVa2nc5l2cGrbDqRQ5XFypMJ7fnj+OhGr18IIYRoTVpNFQtVVSnIKr+5O3ztbCH+Ye6M+0UMWr2G9j398fJ3I7SzD/7hHg6pEqBaVKwV1Wg9XLCWmylccR59sDveY2uqULTCFIq7+eToJ/zryL/YM3UPGqVuaQVaHx8AqnNyUBQFXWDgD9+g0cCDf4eyXFj5S3BvA11GNmqdN4LjKlMFp3ensGfZYjr26c+Qx2fiExxy832KohAREUFERASZmZmcOXPmZnB8+PBhwsPD8ff3r3UOvVbDiKggRkQFUVRezeqj14gMsKUAXckv543lR5kYF87IHkEYXe7JP2MhhBDCad0TO8iqVaUotwKfINvNS2v+eYT0I3kAGL1cCO3iQ7sof7oPDLnTMM3iRgpF+cFsXMI9CXjSVh+5Oq8CvewW39Fnxz7jgwMfkDo1FaO+7jeqWSsqODdsOB6D7iP0L3+p/U2VJTDnJ1CSBS8eBr19fhfm6mrS1q5gz7LFWM3V9BmXTP8Jk9C7/nhTkMrKSt5//30qKyuJiooiKSmJ0NDQOs+5+/x1XvvqMBmFFbi7aBnTM4TkuHD6d/CTknFCCCHEbVpMioXVYiX3cqltd/hcIZnnbE05Zn4wCL1By/mDOVSWmwnt7IN3oJtT5GWWH86lZMfVH6RQuPcJwi2q9h1C8e8Wn1rM26lvs/mRzQQaA+9+wC1y/vY+12fPJuKrr3Dr+SNpCKU5UJoNwT3tsNrbhs6/zo6Fczi3fw8zPpiFh6/fHd9fUlJCamoq+/bto7KyksjISEaPHv2jTUduZ7Wq7EvPZ2naVdYezcJUbSH1jeH4exioqLLg1ox59UIIIYQzu2cDZEu1lez0YvzDPTC46Ti06TI7vz4HgE+QkdBO3oR29iEyrg16J/mHX7WomM4W4NrJB0Wnofi7y1Qcy8MYHyQpFA206vwq3kh5g1UTVhHhHVGvYy2lpZwfOQqXyA60nzfv7l+aDsyBLg+AZ1CD11ubssIC3H18UVWVrXNn02PIiDvezGcymdi/fz+pqanMmDEDPz8/ysvLcXV1vWupuBsqqiwculJIQkfbl7FJs3ZTZbYyMS6Mcb1D8THKuSiEEKL1umcC5Pj4Puo3CzbYdojPFJJ9sRiL2cron0XTMa4NRbkV5FwqJrSzD+7eztVO2ZZCkU15Wg7W0mr8p3XHLToA1aKiaB2/k30v23x5My9ueZEvx35JD/8e9T6+4MvFZP3hD4R9+L94jbxDnnHRVfh7X/DvBNPXgOvdb5qrr8LsLBb+xyuYSkvpNWI0iY9Ou5m7XBur1XozIF6wYAH5+fkkJibSq1cvdLq65xirqsonOy7y9YGrnM4uQa9VGN4tiOmJEQyIlKsZQgghWp97JkCO7R2nzkx4D0WBgLaeN0uuhXXxafKmHA1lKa0ib87xH6ZQxAfh2tUXpQk767Um5wrOsfDUQmb0mEFbr7Z3P+A2qtnMxeSJeAwZQptXXr7zm89uhIWPQof7YOpXoLP/LquptJRdXy/g0Po1GNyMDHx0Gr1HPIDm9qYmtzl27BgpKSlkZWXh6elJQkIC8fHxGAx1/7KoqionMotZlpbBikMZvDC0E9MTO1BiquZCbhm9wu9Q+UMIIYRoQe6ZALlPnz7qsrnrCYr0xuDmnHfg30ihsJZU4d43GFVVuT7/JIYO3pJC4cSsJhOaO9wg9wMHF8CKn0PPSfDQLFvFiyaQdzmdLXP/RUFWJjPe/wi94e7rU1WV8+fPk5KSQnp6OsOGDWPQoEENmt9ssWK2qrjqtSzed5nfLD1Kx0B3kuPCeSg2jFAfuXlUCCFEy3VPBciObjX9Y6qzyihLy6b8YA7Wkmp0AW4EvRovu23NxKpasapWdJrGfXEynTyJLjgYna/vnd+4/T3Y/DbM+BbaJzRqzjtRVZWywgI8fP0wV1Wxbf5n9H0wGa+Au9+Ud+XKFfz9/TEajZw6dYqLFy+SkJCAT02Ju/ooqqjm26OZLE27yr70AhQFEiL9+eTJPlIuTgghRIskAXIjFW++TPGGS5JC4SA55TkM/2o4bw54k0ldJzV4HHNuLmeHDcf3kUcI/t2bd36zqkLmIQiNbfB89XX15DGWvvM7UBT6TXiYvuMmonOp2xWJ7du3s3XrVgB69uxJYmJinStf3O7S9TKWH8zgTHYJ/3zM1uhk3p5LdPB3J6GjP1opGSeEEKIFkAC5HlSLiulMPuVpOXjcF4ahnRdV10qpvFAkKRQOUlpVSsKiBF6Nf5Xp0dMbNVbmH/9I4ZKviFy5AkPHjnU76PxmqCiE6ORGzV0Xxbk5bJv3KWdSd+LdJojBT8ykU58BdbpSUVhYyJ49ezhw4ADV1dX069ePMWPGNHpN1RYrA/+8mdySSkK8XZkQG8bEuDA6tfFs9NhCCCGEo0iAXAfVWTVVKA7aqlBo3PX4jO+IsVf96u4K+7OqVnp/0Zvnej/Hz2N+3qixzPn5nB85CmN8PG1nfXz3A1QVvhgPl3bBtKUQObhR89fV5WOH2fz5LFzc3Jjy1l9R6pEHXV5ezt69e/Hz86NXr15UVVVx6dIlOnXq1OCUIFO1hU0ns1mWlsG2M7lYrCq/GxvFU0kdGjSeEEII4WitptV0fd0owaaareTMOoJaacG1+y0pFFpJoXAGGkWDm86NsuqyRo+l8/Mj4Llnyfnre5Tu3IlHYuKdD1AUmDQXPnsAvnwMnvq2SRqK3K5ddG+eePf/KC8uQtFoKC8qZN+qZfR/aBKu7h53PNZoNDJkyJCbz48cOcLq1asJCgoiKSmJqKgotHepmHE7V72Wsb1CGdsrlNySSlYevsaQrrYvj9vP5DJvzyUmxoUxtFsbDDrnqEkuhBBC2FuLDZBvplAcyKY6t4Kgl+JQdBr8p3VHH2SUFAon5a53t0uADOA7bRpF33xD9dWMuh3g5gvTvoZPR8L8h+GnG8C3vV3WcicarfZm5730w2nsX72cE9s3kzTlCaIHj6jzrnJMTAxarZadO3eydOlSNm/ezMCBA4mPj69z05FbBXoa+OktO8cF5VUcvlLIxhPZeLvpGdfb1uI6tq2P3MQqhBCiRWlxKRbmvApKUzN/kEJhjAnEa1QEGifpwid+3Owjs2nn1Y5REaPsMp5qNqPUo9EGADkn4bNR0O8ZGPYfdllHfWRfOMfmz2dx7cxJgiI7M2zGM4R26Vbn461WK6dPnyYlJQWNRsNTTz2FoihYLJZ67yjfzmJVSTmXx7K0q6w/noWv0YWU3wxDq1EorTTjYWix37mFEELco1ptDrKlrBpFAY1RT/nRPPIXnZIUCnGTqqqUbtmKsV8/tB7udTso/yL4RthSLxxAVVVOpWxl24LPCe8ezdgXf92gMUwmE25ubpSWlvLRRx8RExPDgAED8PRs/I13JaZq0vPK6RnujbnmBr8OAe5MjAvngZ7BeLo6Z9MfIYQQrUurCpBVixXT6QLKD2RTcSofr2Ht8BreDtVsxWoySwrFPcpkNlFpqcTb4G23MSvPnuXCuAfxf/YZ2rz0Uv0Ovn4e9nwEo/8M2ubfHa2qKMdcXY3Ry5u8y+lcPHSAuDEPotXVL/gsLCxk48aNnDhxAo1GQ0xMDAMHDsTf3z7tpyuqLHyacoGlaRlczCvDVa9hZFQwzwyOpEeo/X6XQgghRH21igBZVVWK16dTtj/7+xSK2Da49w1CH1TH3UHhtF747gVyynNYMm6JXcfN+NWvKdmwgY7frkUfGlr3Aw/MhVW/hLgnYNyHDttRBti5ZAF7li7CNySModN/RoeY+HqPcf36dXbt2sWhQ4dQVZWXX37ZLrvJN6iqysErhSxLu8qqw5n887E4EjsFkFFYQYmpmm7BXnabSwghhKiLFhsgW8qqqTxfeLMU2/UFJ8GqYpQUihbn19t/zfG846xJXmPXcauvXeP8A2PwvP9+wt77a/0O/u4t2PE3GPxbGPq6XddVXxcO7mPr3NkUZF4jMr4fQ56YiW9wPQL+GiUlJZw/f56YmBjA1oCkbdu2RERE2O2Gu0qzBb1Gg0aj8M6aE8zecZGoEC+S48IYHxNGoKfBLvMIIYQQd9KiyrzdnkKBRcWlnRc6HwN+U7vJXfMtlFFntFsVi1vpQ0PxmzGd6x/Pwu/xabj17l33g4e9CSVZsO3P4BkMfWbYfX11FRnbl/Y9Y0hbu5LdS7/k+NZNJE1+ot7jeHp63gyOKysr2bt3L5s3byYsLIykpCS6du3aoMoXt7q1DNyzgzsS5uPGsoMZvL3mJP/97SkeiA7m/6bEyt+yEEIIp+OUAXLlxSKuLzhpS6Hw0OOREIoxPgidj23HSf5Bbbnc9e6Um8ubZGz/mU9Ttn0HlsLC+h2oKDDuf6E0Bw5/aUu30DiuIopWp6fvgxPpft9QXNzcAFvDkbKiQroNHFTvvw+DwcCLL77IoUOH2LVrF4sXLyYgIIDk5GRC65OOcgf+HgamJ3ZgemIHzmaXsOxgBlarenOtH2w8Q1LnAPq095W/byGEEA7nFAGypayaikM5aH1dcYvyR9fGiCHCC2OcpFC0Nu56dyrMFVisFrR2DkK1Hu5ELP26YQGYVm9rJAIODY5vdaN2MsCRTes4vXsHhzesYdiMZ2kTEVmvsfR6PX379iUuLo4TJ06QmpqKl5ctXzg/Px8PDw9cXOxz42vnIE9+M/r7snWZRRXM3nGB//3uLO38jCTHhZEcG047f6Nd5hNCCCHqy2E5yPtS92I6XUDZgWxMNSkU7n2D8Z3YudnXI5xHWnYaB3MO8kSPJ9BrmqZMmFpVReGy5Xg/NAGNoQF5sKZiWPkLGPoGBHa1/wIbwGq1cGzLJlIWzcVUWkqvEaMYOGkaRq/GV5D49NNPycvLo3///vTr1w+j0f6Ba1mlmXXHslh28Cq7zl9HVeGz6X0Y1i3I7nMJIYRoXe6pm/S+fe5zKs8WovHQY4xpgzE+CJcQqUIhml75vn1cevwJ2rz2Kv4zZ9Z/gIJL8MkI0BngpxvBK8T+i2wgU1kpu79ayMH1q7n/6RfoOWxko8e8cuUKKSkpnD59Gr1eT3x8PAkJCXh7N035tmuFFXxzKIMnEyJwN+j4Ync6qRfzeTgunPs6B6CTK0pCCCHq4Z4KkHcs2AAWVVIoxA+YzCZyK3JpY2yDQdt0VQ6uPPdzyvfto+P6degaUgs48zB8PsbWTGTGWnB1rlq/+deu4hMcgkaj5cyeFNw8vWjbo1ejxszJyWHnzp0cPXqUUaNG0b9/fzut9s7+tf08H209T0F5NQEeBsbHhJIcFyb1lYUQQtTJPRUgN1WraXFv23ZlGy9sfoGFYxbSM7Bnk81TeeEiFx58EJ9HHibk979v2CDnN8OCR6BdAkxbattRdjKqqjL/9ZfIuXieLgn3MXjaDLwC2jRqzMLCQoxGIy4uLhw4cICzZ8+SlJREeHi4nVb976rMVraezmFZWgbfncqmfwd/5s+0BehFFdV4u0nXPiGEELVrUWXeROtk1NvyW8vM9i/1ditDZAd8J0+mYOFC/KZOxdC5AbnvHYfBhI9g4++hOAP86ndjXHNQFIXJb73L/pXL2Lviay4c2Eu/CQ/TZ1wyepeGBfQ+Pj43H1ssFtLT0zl16hQREREkJSXRsWNHu1eicNFpGNkjmJE9gikoqyK/vAqAnBITSX/eQkJHf5LjwhgZFYybi3PcRCmEEOLeJQGycCruelseelPUQr5dwPM/p/LcOaxVVQ0fpNck6DoGDB5w42qMk5Up07sYSHh4Cj2GDGfb/M/ZtWQBYV170C66cSkXAP369aN3796kpaWxa9cu5s+fT+/evXnooYfssPLa+bq74Otuq6ihURSeGRzJsrQMXvzyEB4GHWN6BvOLYZ1p6ydVMIQQQjSMpFgIp3Kp+BJjl4/lv5L+i3Edxzl6OXVntcL6N2w37CW+6OjV3FHu5XQC20UAcHTLBkI7d8M/vF2jxzWbzRw9ehRPT086depEeXk5J06coHfv3uj1TZsCYbWqpF7MZ1naVdYdz2LDy4MI8XbjZGYxrnotHQLkBmAhhGitJMVC3POacwf5BkthIQVffon/zJkoukb8SZRmQ+pH4BEEvSfbb4F2diM4rjaZSFn0BRUlxcSOHkfCw1Nwdfdo8Lg6nY7Y2Nibz0+cOMHq1avZunUrAwYMoE+fPri6ujZ2+bXSaBQSOvqT0NGfdx7qiYvOduPvu+tOseV0LnHtfEiOC2dsrxB8jPap5yyEEKLlkh1k4VSqLFV8deYr+gb3pYtvl2aZs3jDBjJ++SLBf/gDvpMfbfhA5kqYPxEu74apS6DTcPstsomUFxexc/E8jny3HjdPL+6b8iTRQ0agNLLNNNhuEExPT2fHjh1cuHABg8FA3759GTZsWKPbWNdVVpGJFYcyWJp2lTPZpbhoNUxPjOCNMd2bZX4hhBCOJ1UshGgAVVW5/PgTVF64QMcN69F6NHwXFVORrfxbQTpMXw2hsXc9xBlkXzzP5s9nkXXuNNPf/wjfYPu0mL7h2rVrpKSkYLFYmDJlCgBlZWW4uzdP6oOqqhy/VsyytAwiA92ZNqA9pmoL760/zfiYMKLDvKTFtRBCtFASIIsW4ULhBQw6A2EeYc02Z8Wx46Q//DD+T8+kzauvNm6w4kyYOw7u/yN0+4l9FtgMVFUlJ/0CQR06AnBw3So690/8QUvrxrJYLGi1WvLz8/nHP/5B9+7dSUpKIjg42G5z1NW+9Hwe+ySVKrOVzm08SI4LZ0JsKCHebs2+FiGEEE1HAmTRIgxfMpzEsETeSnyrWee99pvfUrx2LZHfrsWlsTV9LdWgrbkxzWqFZkopsJeinGw+f/kZNDo9CRMnEzfmQbQ6+91oV1ZWxs6dO9m/fz9VVVV06tSJpKQk2rdv36w7uUXl1aw5msmytKvsv1SAosCmVwbTMbARVxGEEEI4FQmQRYswbvk4uvh24W9D/tas81ZnZ5Pzl7/Q5tVX0YfZaff68Jew/zOYtsxWCu4eUpB1ja1ffMKFA3vxDQlj6JNP0yG2Xp8vd1VRUcG+ffvYs2cPJpOJV155BY/GpLg0QnpeGd+dyuGpxAgUReGPq45TXGFmYlwYAyL90WgkBUMIIe5FEiCLFmHy6sn4uPrw8YiPHb2Uxju1FhY/ZmsqMuXL73eV7yEXD+5ny9zZVBQXMfPvn2Ew2r++cHV1NVeuXCEy0tZsZdWqVbRt25aePXui1Tqm8cfbq0+weN8VSirNhHq7MiE2jInx4bK7LIQQ95iGBMj31nVf0Sq4690pry532PyVFy+S/de/olqtjR+s2xgY+wGc2wQrf/l9M5F7SIfYPjz53t95+M13MBiNqFYraWtXUGWqsNscer3+ZnBsMpm4cuUK33zzDR9++CF79uyhqjHNXBroP8dGse8/R/B/U2LpEuzJx9vOM2/3JcBWdzm/rPnXJIQQonlIHWThdIx6I5mlmQ6bvyLtIPmffoZr9yi8x9rhJrv46VCSBVv/29ZIZPjvGj9mM9Pq9Ddv3rt66jhb5s5m38qlDHpsBt2Shtg1b9jV1ZXnnnuOs2fPkpKSwrp169i2bRtTp06lbdu2dpunTmvRaxnXO5RxvUPJKTHd/H5z4wa/od3aMDEunKHdAjHopMW1EEK0FJJiIZzOvqx9VJgrGBQ+yCHzq1YrFx9+GEthIR3XrkVjj+YWqgqrX7I1ERnyutO1o66va2dOsfnzWWRfOEto1yiGTf8ZQZGdmmSuy5cvk5qayoMPPojBYODq1at4enri7e3dJPPVxZX8cr7Ync43h66RW1KJj1HPuF6hvDayK97Gey+NRgghWjLJQRbCTsr2pHJ5+nQCX36ZgGd+Zp9BVfX7wNhcCTqDfcZ1ENVq5di2TexYOBdXD09m/O2fdmkwcsc5VZWPP/6Y3NxcevXqRWJiIoGBgU06552YLVZSzuWxLC2D/en5bP3VUFx0GlIvXCfcz0iYj5SME0IIR5MAWbQImaWZXC65TP+Q/g5dx5XnX6B89246bliPLiDAfgNnHoFFkyF5NkQk2m9cBzGVlVJyPY/AdhFUm0ycTNlK9ND70TTRzXUFBQXs3r2btLQ0zGYz3bp1Y/DgwYSEhDTJfHVltljRaTWoqsqgv27hSn4FCZH+JMeF8UDPEDwMktEmhBCOIDfpiRZhxfkVzNwwE7PV7NB1BP3qNXweeQTFxcW+A3uHg4s7LJoC2SfsO7YDuLp7ENguAoBTu7azcfbfmfebX3L52OEmmc/X15cxY8bw0ksvMWjQINLT08nNzQVsjUgc8aUfQKe1fZwqisLCmQN45f4uZBZV8Kuvj9Dn7Y3M2XnRIesSQghRf7KDLJzOvBPzeHffu6RMTsHb4Lg80yZVeBk+uR8UDczcaAuaWwBVVTm3fw9b535CcW42XfonMvjxn+IV2KbJ5qysrESn06HVaklJSeH48eMkJSXRvXt3NA5u0KKqKmmXC1madpVRPYIZ3CWQ9LwyFu29zMT4cLoEeTp0fUII0Ro0ZAdZrvkJp+OudwegvLrcKQLksr17Kdm4iaA3XrdftQafdjDta/h8DMyfCE+tAzdf+4ztQIqi0LlvAhG94ziwajmp33xFVaWJia//scnmNBi+z+X28fGhqqqKr776Cj8/PxITE+nduzc6nWM+6hRFIb69L/Htv//dpl0u4JOUi8zafoHoMC+SY8N5MCaUAI97OyddCCFaEkmxEE7HqLc1oiirLnPwSmwqT52iYN48yrZvt+/AwT1h8gII7AY6O1TKcCJ6FwMDJk5mxgcfM2zGMwCU5OdxJnVnk6ZAREdH8/zzzzNp0iQMBgOrVq1i+fLlTTZfQyTHhZP6xnB+Py4KBYW3Vp9g0LtbqKiyOHppQgghasgOsnA6Rl1NgGx2jgDZd/JkChYsJPsv7+I+cCCK3o5lvDoMsv0AVJaA3giallNP1yvg+woTB9etZt+Kr2kX3Yuh058hoG37JplTo9EQFRVF9+7duXjx4s0d5qKiIvbv30///v0d1s76hgAPAzMSOzAjsQNnsks4llGEm4vt9z7j872E+LgxMS6MuHa+dq0xLYQQom4kB1k4nesV1zmWd4yYNjFOkWIBUPLdd1x9/gWCfvcmflOn2n+CqjL4dCS0GwBj3rvn6yTXxmqxcHjTt+xaPJ/KinJiRv2EgQ8/hmszBasHDx5kxYoV6HQ6YmNjGThwIL6+zpXWUm2x8puvj/DtsSwqqi209zeSHBvOxPgwwn3t3+JbCCFaAynzJkQTUVWVy9NnUHn6NB03rEfr5WX/STa8Cbs+hGFvwqDX7D++kygvLmLXkvkc3rSOmJE/YfhTzzbb3Hl5eezatYtDhw6hqiq9evViwoQJTrdLW1ppZt2xLJalXWX3hev8aXw00wa0p7zKjNmq4uUqzUiEEKKuJEAWLYLJbGL3td108u1EW8/mbS18J6aTJynffwDfyY/aN83iBqsVvnkWjiyG8f+A2Gn2n8OJ5KRfwN3HF3cfX3IvXaTKZCKsa/dmmbu4uJg9e/ZQVVXF2LFjAcjKyiIoKMjpguWMwgq8XHV4uuqZv+cSf1p9gpE9gkmOC+O+TgE3y8sJIYSonQTIokW4XnGdIUuG8Hq/15navQnSGZyZuQoWPQoXtsFjS6DTCEevqFmsfP+/OJu6i6j7hnLf1Ol4+Pk36/yZmZnMmjWLtm3bkpSUROfOnR1eIq42p7KKWZh6mZWHr1FYXk2Ah4EJMaG8PqY7Wo1zBfZCCOEspFGIaBFulnkzlzt4JbUrWrmSrLf+1DSD61xg0hcQPdFW3aKVGP3zl+n/0KOc3r2Dz15+lr0rvsZcXd1s8/v7+zNmzBiKi4tZtGgRH3/8MYcPH8Zica7KEt2CvXhrfDSpbwzn42nxxLXz4WhG0c3geOOJbHJKTA5epRBC3PsaVcVCUZQ/AE8DuTUvvaGq6trGLkq0bgatAa2idZoyb7erunqVgoUL8frJGIzx8fafwOAJE2fbHlstUJYLnsH2n8eJuLi6kTT5caKHjGDrvE/ZsXAOOr2euDHjm2d+Fxf69etHfHw8x48fJyUlhTVr1tClSxfc3NyaZQ31YdBpGR0dzOjoYCxW21XAElM1zy9Iw6Kq3Nc5gOS4cEZGBeGqbzlVUYQQork0KsWiJkAuVVX1vfocJykW4m4GLhrI2MixvNH/DUcv5d9YKyo4P/oBdIGBRCxZjNKUl+JXvQTnN8NPN4JnUNPN42QuHTlEWLcodC4uXD11HHdvH3xDwpptflVVuX79OgEBAaiqyrx582jfvj39+vVzyoD5hnM5pSw/eJXlaRlcKzLhadDx3qTejOrRsr9gCSHEnUiKhWgx3PXuTruDrHFzo80rL2M6dozi1aubdrLYx207yAsfsdVJbiXa94pB5+KCqqps/vQj5rz6PNsXzqGqonnSbhRFISAgALC1stZqtWzZsoUPPviA9evXU1xc3CzrqK9ObTz41ahupPxmGAuf7s+o6OCb7ax3ncvj/Y1nSM9zzr8rIYRwJvbYQZ4OFAP7gVdVVS2423Gygyzu5kjuEbwN3rT3appmEo2lWq2kT3oUc14eHdd9i8a1CTvhnd0ICx+1NRSZusSWp9yKlBUWsGPhXI5v24S7rx+DHptB96QhzV5tIisri507d3Ls2DEUReHJJ5+kfXvnPD9r8+F3Z/lg0xlUFeLb+5IcF8bYnqF4G6VknBCiZWuSKhaKomwCars+9x/AHiAPUIE/ASGqqj71I+P8DPhZzdNo4Fh9FipahQBs55MQt5LzQtRGzgtRGzkvRG26qqrqWZ8D7FbmTVGUCGC1qqrRdXjv/vpG8qLlk/NC1EbOC1EbOS9EbeS8ELVpyHnRqBxkRVFCbnn6ELIrLIQQQggh7nGNKvMGvKsoSgy2FIt04JnGLkgIIYQQQghHalSArKrq4w089F+NmVe0WHJeiNrIeSFqI+eFqI2cF6I29T4vHNJqWgghhBBCCGcldZCFEEIIIYS4hcMCZEVR/qAoSoaiKIdqfsY4ai3CsRRFGa0oymlFUc4pivJbR69HOAdFUdIVRTla8/kghdNbKUVRPlMUJUdRlGO3vOanKMpGRVHO1vzX15FrFM3vR84LiStaOUVR2iqKskVRlJOKohxXFOXFmtfr/Znh6B3kD1RVjan5WevgtQgHUBRFC/wDeACIAqYoihLl2FUJJzK05vNByja1XnOA0be99lvgO1VVOwPf1TwXrcsc/v28AIkrWjsztqZ13YEBwPM1MUW9PzMcHSAL0Q84p6rqBVVVq4AvgfEOXpMQwkmoqrodyL/t5fHA3JrHc4EJzbkm4Xg/cl6IVk5V1UxVVdNqHpcAJ4EwGvCZ4egA+QVFUY7UXCqRS2StUxhw5ZbnV2teE0IFNiiKcqCmE6cQNwSpqpoJtn8QgTYOXo9wHhJXCOBmA7tYIJUGfGY0aYCsKMomRVGO1fIzHvgI6AjEAJnA35pyLcJpKbW8JqVVBECiqqpx2NJvnlcUZZCjFySEcGoSVwgAFEXxAJYCL6mqWtyQMRrbKOSOVFUdUZf3KYoyG1jdlGsRTusq0PaW5+HANQetRTgRVVWv1fw3R1GU5djScbY7dlXCSWQrihKiqmpmTUfXHEcvSDieqqrZNx5LXNF6KYqixxYcL1BVdVnNy/X+zHBkFQtpUy0A9gGdFUXpoCiKCzAZWOngNQkHUxTFXVEUzxuPgZHIZ4T43krgyZrHTwIrHLgW4SQkrhCKoijAp8BJVVXfv+V/1fszw2GNQhRFmYftMsjNNtU38kNE61JTiud/AC3wmaqq7zh2RcLRFEWJBJbXPNUBC+W8aJ0URVkEDAECgGzg98A3wBKgHXAZeERVVblhqxX5kfNiCBJXtGqKoiQBO4CjgLXm5Tew5SHX6zNDOukJIYQQQghxC0dXsRBCCCGEEMKpSIAshBBCCCHELSRAFkIIIYQQ4hYSIAshhBBCCHELCZCFEEIIIYS4hQTIQgghhBBC3EICZCGEEEIIIW4hAbIQQgghhBC3+H8SV45WdND2/AAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# we first turn each vector 90 degrees to represent our hyperplane edge\n",
    "# (currently they are normal to the hyperplane - which is good for dot product but bad for visualizing)\n",
    "def turn90(vec):\n",
    "    return -vec[1], vec[0]\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "for norm in hash_vecs:\n",
    "    hyperplane = turn90(norm)\n",
    "    # extend range of points so we see split across the chart\n",
    "    hyperplane = [hyperplane[0]*-1000, hyperplane[0]*1000], [hyperplane[1]*-1000, hyperplane[1]*1000]\n",
    "    # and plot\n",
    "    plt.plot(hyperplane[0], hyperplane[1], '--')\n",
    "\n",
    "plt.scatter(points[:,0], points[:,1])\n",
    "plt.xlim(-5, 20)\n",
    "plt.ylim(-5, 22)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that most of our hash function splits are at an angle to our vectors as to not be particularly helpful. This is typical and not really an issue, the usual solution is to increase `nbits`. However, if we would like to - this issue can be solved by simply centering our data around the origin point.\n",
    "\n",
    "All we do is take the average value of each dimension in our data, and subtract from our vector dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "points = points - points.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-10.0, 10.0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "for norm in hash_vecs:\n",
    "    hyperplane = turn90(norm)\n",
    "    # extend range of points so we see split across the chart\n",
    "    hyperplane = [hyperplane[0]*-1000, hyperplane[0]*1000], [hyperplane[1]*-1000, hyperplane[1]*1000]\n",
    "    # and plot\n",
    "    plt.plot(hyperplane[0], hyperplane[1], '--')\n",
    "\n",
    "plt.scatter(points[:,0], points[:,1])\n",
    "plt.xlim(-10, 10)\n",
    "plt.ylim(-10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have a much better split. Let's go ahead and create our binary hash values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "00110010\n",
      "11001101\n",
      "11001101\n"
     ]
    }
   ],
   "source": [
    "for xy in points:\n",
    "    binary_hash = ''\n",
    "    for h_vec in hash_vecs:\n",
    "        binary_hash += str(direction(xy, h_vec))\n",
    "    print(binary_hash)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have our three hash functions, and from this we can identify that vectors *2* and *3* are both being identified as strong candidate pairs and assigned the exact same hash code - which is exactly what we want!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.13 (default, Mar 28 2022, 06:59:08) [MSC v.1916 64 bit (AMD64)]"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "5fe10bf018ef3e697f9035d60bf60847932a12bface18908407fd371fe880db9"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
